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## Wave Equation (wave + equation)
Kinds of Wave Equation
## Selected Abstracts## On supersymmetry and other properties of a class of marginally deformed backgrounds FORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5-6 2006R. HernándezAbstract We summarize our recent work on supergravity backgrounds dual to part of the Coulomb branch of ,, = 1 theories constructed as marginal deformations of ,, = 4 Yang,Mills. In particular, we present a summary of the behaviour of the heavy quark-antiquark potential which shows confining behaviour in the IR as well as of the spectrum of the wave equation. The reduced supersymmetry is due to the implementation of T-duality in the construction of the deformed supergravity solutions. As a new result we analyze and explicitly solve the Killing spinor equations of the ,, = 1 background in the superconformal limit. [source] ## A 2-D spectral-element method for computing spherical-earth seismograms,II. GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2008Waves in solid, fluid mediaSUMMARY We portray a dedicated spectral-element method to solve the elastodynamic wave equation upon spherically symmetric earth models at the expense of a 2-D domain. Using this method, 3-D wavefields of arbitrary resolution may be computed to obtain Fréchet sensitivity kernels, especially for diffracted arrivals. The meshing process is presented for varying frequencies in terms of its efficiency as measured by the total number of elements, their spacing variations and stability criteria. We assess the mesh quantitatively by defining these numerical parameters in a general non-dimensionalized form such that comparisons to other grid-based methods are straightforward. Efficient-mesh generation for the PREM example and a minimum-messaging domain decomposition and parallelization strategy lay foundations for waveforms up to frequencies of 1 Hz on moderate PC clusters. The discretization of fluid, solid and respective boundary regions is similar to previous spectral-element implementations, save for a fluid potential formulation that incorporates the density, thereby yielding identical boundary terms on fluid and solid sides. We compare the second-order Newmark time extrapolation scheme with a newly implemented fourth-order symplectic scheme and argue in favour of the latter in cases of propagation over many wavelengths due to drastic accuracy improvements. Various validation examples such as full moment-tensor seismograms, wavefield snapshots, and energy conservation illustrate the favourable behaviour and potential of the method. [source] ## A one-way wave equation for modelling seismic waveform variations due to elastic heterogeneity GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2005D. A. AngusSUMMARY The application of a new one-way narrow-angle elastic wave equation to isotropic heterogeneous media is described. This narrow-angle finite-difference propagator should provide an efficient and accurate method of simulating primary body wave(s) passing through smoothly varying heterogeneous media. Although computationally slower than ray theory, the narrow-angle propagator can model frequency-dependent forward diffraction and scattering as well as the averaging effects due to smooth variations in medium parameters that vary on the sub-Fresnel zone level. Example waveforms are presented for the propagation of body waves in deterministic as well as stochastic heterogeneous 3-D Earth models. Extrapolation within deterministic media will highlight various familiar wave-diffraction and pulse-distortion effects associated with large-scale inhomogeneities, such as geometrical spreading, wavefront folding and creeping-wave diffraction by a compact object. Simulation within stochastic media will examine the effects of varying the correlation lengths of random heterogeneities on wave propagation. In particular, wave phenomena such as frequency-dependent forward scattering, the appearance of random caustics and the generation of seismic coda will be shown. [source] ## Velocity analysis based on data correlation GEOPHYSICAL PROSPECTING, Issue 6 2008T. Van LeeuwenABSTRACT Several methods exist to automatically obtain a velocity model from seismic data via optimization. Migration velocity analysis relies on an imaging condition and seeks the velocity model that optimally focuses the migrated image. This approach has been proven to be very successful. However, most migration methods use simplified physics to make them computationally feasible and herein lies the restriction of migration velocity analysis. Waveform inversion methods use the full wave equation to model the observed data and more complicated physics can be incorporated. Unfortunately, due to the band-limited nature of the data, the resulting inverse problem is highly nonlinear. Simply fitting the data in a least-squares sense by using a gradient-based optimization method is sometimes problematic. In this paper, we propose a novel method that measures the amount of focusing in the data domain rather than the image domain. As a first test of the method, we include some examples for 1D velocity models and the convolutional model. [source] ## From the Hagedoorn imaging technique to Kirchhoff migration and inversion GEOPHYSICAL PROSPECTING, Issue 6 2001Norman BleisteinThe seminal 1954 paper by J.G. Hagedoorn introduced a heuristic for seismic reflector imaging. That heuristic was a construction technique , a ,string construction' or ,ruler and compass' method , for finding reflectors as an envelope of equal traveltime curves defined by events on a seismic trace. Later, Kirchhoff migration was developed. This method is based on an integral representation of the solution of the wave equation. For decades Kirchhoff migration has been one of the most popular methods for imaging seismic data. Parallel with the development of Kirchhoff wave-equation migration has been that of Kirchhoff inversion, which has as its objectives both structural imaging and the recovery of angle-dependent reflection coefficients. The relationship between Kirchhoff migration/inversion and Hagedoorn's constructive technique has only recently been explored. This paper addresses this relationship, presenting the mathematical structure that the Kirchhoff approach adds to Hagedoorn's constructive method and showing the relationship between the two. [source] ## One- and two-dimensional modelling of overland flow in semiarid shrubland, Jornada basin, New Mexico HYDROLOGICAL PROCESSES, Issue 5 2006David A. HowesAbstract Two distributed parameter models, a one-dimensional (1D) model and a two-dimensional (2D) model, are developed to simulate overland flow in two small semiarid shrubland watersheds in the Jornada basin, southern New Mexico. The models are event-based and represent each watershed by an array of 1-m2 cells, in which the cell size is approximately equal to the average area of the shrubs. Each model uses only six parameters, for which values are obtained from field surveys and rainfall simulation experiments. In the 1D model, flow volumes through a fixed network are computed by a simple finite-difference solution to the 1D kinematic wave equation. In the 2D model, flow directions and volumes are computed by a second-order predictor,corrector finite-difference solution to the 2D kinematic wave equation, in which flow routing is implicit and may vary in response to flow conditions. The models are compared in terms of the runoff hydrograph and the spatial distribution of runoff. The simulation results suggest that both the 1D and the 2D models have much to offer as tools for the large-scale study of overland flow. Because it is based on a fixed flow network, the 1D model is better suited to the study of runoff due to individual rainfall events, whereas the 2D model may, with further development, be used to study both runoff and erosion during multiple rainfall events in which the dynamic nature of the terrain becomes an important consideration. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## The control-theory-based artificial boundary conditions for time-dependent wave guide problems in unbounded domain INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2005Tianyun LiuAbstract A method is proposed to obtain the high-performance artificial boundary conditions for solving the time-dependent wave guide problems in an unbounded domain. Using the variable separation method, it is possible to reduce the spatial variables of the wave equation by one. Furthermore, introducing auxiliary functions makes the reduced wave equation a linear first-order ordinary differential system with one control input. Solving the closed-loop control system, a stable and accurate artificial boundary condition is obtained in a rigorous mathematical manner. Numerical examples have demonstrated the effectiveness of the proposed artificial boundary conditions for the time-dependent wave guide problems in unbounded domain. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Numerical error patterns for a scheme with hermite interpolation for 1 + 1 linear wave equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2004Zuojin ZhuAbstract Numerical error patterns were presented when the fourth-order scheme based on Hermite interpolation was used to solve the 1 + 1 linear wave equation. Since most non-linear equations for real systems can be converted into linear forms by using proper transformations, this study certainly pertains its practical significance. The analytical solution was obtained under inhomogeneous initial and boundary conditions. It was found that not only the Hurst index of an error train at a given position but also its spatial distribution is dependent on the ratio of temporal to spatial intervals. The solution process with the fourth-order scheme based on Hermite interpolation diverges as the ratio is greater than unity. The results show that regular error pattern and smaller maxima of absolute values of numerical errors can be obtained when the ratio is set as unity; while chaotic phenomena for the numerical error propagation process can appear when the ratio is less than unity. It was found that it is better to choose the ratio as unity for the numerical solution of 1 + 1 linear wave equation with the scheme; while other selections for the ratio in the scheme can bring about chaotic patterns for the numerical errors. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003K. DjidjeliAbstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Hybrid finite element/volume method for shallow water equations INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Shahrouz AliabadiAbstract A hybrid numerical scheme based on finite element and finite volume methods is developed to solve shallow water equations. In the recent past, we introduced a series of hybrid methods to solve incompressible low and high Reynolds number flows for single and two-fluid flow problems. The present work extends the application of hybrid method to shallow water equations. In our hybrid shallow water flow solver, we write the governing equations in non-conservation form and solve the non-linear wave equation using finite element method with linear interpolation functions in space. On the other hand, the momentum equation is solved with highly accurate cell-center finite volume method. Our hybrid numerical scheme is truly a segregated method with primitive variables stored and solved at both node and element centers. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Matrix-free GMRES iterative solvers are used to solve both the wave and momentum equations in finite element and finite volume schemes. Several test problems are presented to demonstrate the robustness and applicability of the numerical method. Copyright © 2010 John Wiley & Sons, Ltd. [source] ## A space,time discontinuous Galerkin method for the solution of the wave equation in the time domain INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2009Steffen PetersenAbstract In recent years, the focus of research in the field of computational acoustics has shifted to the medium frequency regime and multiscale wave propagation. This has led to the development of new concepts including the discontinuous enrichment method. Its basic principle is the incorporation of features of the governing partial differential equation in the approximation. In this contribution, this concept is adapted for the simulation of transient problems governed by the wave equation. We present a space,time discontinuous Galerkin method with Lagrange multipliers, where the shape approximation in space and time is based on solutions of the homogeneous wave equation. The use of hierarchical wave-like basis functions is enabled by means of a variational formulation that allows for discontinuities in both the spatial and the temporal discretizations. Numerical examples in one space dimension demonstrate the outstanding performance of the proposed method compared with conventional space,time finite element methods. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Fully hierarchical divergence-conforming basis functions on tetrahedral cells, with applications INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2007Matthys M. BothaAbstract A new set of hierarchical, divergence-conforming, vector basis functions on curvilinear tetrahedrons is presented. The basis can model both mixed- and full-order polynomial spaces to arbitrary order, as defined by Raviart and Thomas, and Nédélec. Solenoidal- and non-solenoidal components are separately represented on the element, except in the case of the mixed first-order space, for which a decomposition procedure on the global, mesh-wide level is presented. Therefore, the hierarchical aspect of the basis can be made to extend down to zero polynomial order. The basis can be used to model divergence-conforming quantities, such as electromagnetic flux- and current density, fluid velocity, etc., within numerical methods such as the finite element method (FEM) or integral equation-based methods. The basis is ideally suited to p -adaptive analysis. The paper concludes with two example applications. The first is the FEM-based solution of the linearized acoustic vector wave equation, where it is shown how the decomposition into solenoidal components and their complements can be used to stabilize the method at low frequencies. The second is the solution of the electric field, volume integral equation for electromagnetic scattering analysis, where the benefits of the decomposition are again demonstrated. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## A non-reflecting layer method for non-linear wave-type equations on unbounded domains with applications to shape memory alloy rods INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2005M. NewmanAbstract In this paper a new technique is introduced and applied in solving one-dimensional linear and non-linear wave-type equations on an unbounded spatial domain. This new technique referred to as the non-reflecting layer method (NRLM) extends the computational domain with an artificial layer on which a one-way wave equation is solved. The method will be applied to compute stress waves in long rods consisting of NiTi shape memory alloy material subjected to impact loading and undergoing detwinning and pseudo-elastic material responses. The NRLM has been tested on model problems and it has been found that the computed solutions agree well with the exact solutions, i.e. normalized error levels are in ranges acceptable for engineering computations. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Perfectly matched layers for transient elastodynamics of unbounded domains INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2004Ushnish BasuAbstract One approach to the numerical solution of a wave equation on an unbounded domain uses a bounded domain surrounded by an absorbing boundary or layer that absorbs waves propagating outward from the bounded domain. A perfectly matched layer (PML) is an unphysical absorbing layer model for linear wave equations that absorbs, almost perfectly, outgoing waves of all non-tangential angles-of-incidence and of all non-zero frequencies. In a recent work [Computer Methods in Applied Mechanics and Engineering 2003; 192: 1337,1375], the authors presented, inter alia, time-harmonic governing equations of PMLs for anti-plane and for plane-strain motion of (visco-) elastic media. This paper presents (a) corresponding time-domain, displacement-based governing equations of these PMLs and (b) displacement-based finite element implementations of these equations, suitable for direct transient analysis. The finite element implementation of the anti-plane PML is found to be symmetric, whereas that of the plane-strain PML is not. Numerical results are presented for the anti-plane motion of a semi-infinite layer on a rigid base, and for the classical soil,structure interaction problems of a rigid strip-footing on (i) a half-plane, (ii) a layer on a half-plane, and (iii) a layer on a rigid base. These results demonstrate the high accuracy achievable by PML models even with small bounded domains. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Non-reflecting artificial boundaries for transient scalar wave propagation in a two-dimensional infinite homogeneous layer INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2003Chongbin ZhaoAbstract This paper presents an exact non-reflecting boundary condition for dealing with transient scalar wave propagation problems in a two-dimensional infinite homogeneous layer. In order to model the complicated geometry and material properties in the near field, two vertical artificial boundaries are considered in the infinite layer so as to truncate the infinite domain into a finite domain. This treatment requires the appropriate boundary conditions, which are often referred to as the artificial boundary conditions, to be applied on the truncated boundaries. Since the infinite extension direction is different for these two truncated vertical boundaries, namely one extends toward x ,, and another extends toward x,- ,, the non-reflecting boundary condition needs to be derived on these two boundaries. Applying the variable separation method to the wave equation results in a reduction in spatial variables by one. The reduced wave equation, which is a time-dependent partial differential equation with only one spatial variable, can be further changed into a linear first-order ordinary differential equation by using both the operator splitting method and the modal radiation function concept simultaneously. As a result, the non-reflecting artificial boundary condition can be obtained by solving the ordinary differential equation whose stability is ensured. Some numerical examples have demonstrated that the non-reflecting boundary condition is of high accuracy in dealing with scalar wave propagation problems in infinite and semi-infinite media. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A computational model for impact failure with shear-induced dilatancy INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003Z. ChenAbstract It has been observed in plate impact experiments that some brittle solids may undergo elastic deformation at the shock wave front, and fail catastrophically at a later time when they are shocked near but below the apparent Hugoniot elastic limit. Because this phenomenon appears to have features different from those of usual inelastic waves, it has been interpreted as the failure wave. To design an effective numerical procedure for simulating impact failure responses, a three-dimensional computational damage model is developed in this paper. The propagation of the failure wave behind the elastic shock wave is described by a non-linear diffusion equation. Macroscopic shear-induced dilatancy is assumed and treated as a one-to-one measure of the mean intensity of microcracking. The damage evolution in time is determined based on the assumption that the deviatoric strain energy in the elastically compressed material (undamaged) is converted, through the damaging process, into the volumetric potential energy in the comminuted and dilated material. For the ease in large-scale simulations, the coupled damage diffusion equation and the stress wave equation are solved via a staggered manner in a single computational domain. Numerical solutions by using both the finite element method and the material point method, i.e. with and without a rigid mesh connectivity, are presented and compared with the experimental data available. It is shown that the model simulations capture the essential features of the failure wave phenomenon observed in shock glasses, and that the numerical solutions for localized failure are not mesh-dependent. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Unified formulation of radiation conditions for the wave equation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Steen KrenkAbstract A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choices of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Absorbing boundary condition on elliptic boundary for finite element analysis of water wave diffraction by large elongated bodies INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2001Subrata Kumar BhattacharyyaAbstract In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modelling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers of first- and second-orders, which require a circular cylindrical truncation boundary in the diffraction-radiation problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic cylindrical truncation boundary has the potential to reduce the modelling domain and hence the computational effort. Grote and Keller [On non-reflecting boundary conditions. Journal of Computational Physics 1995; 122: 231,243] proposed extension of the first- and second-order BGT dampers for the elliptic radiation boundary and used these conditions to the acoustic scattering by an elliptic scatterer using the finite difference method. In this paper, these conditions are implemented for the problem of diffraction of water waves using the finite element method. Also, it is shown that the proposed extension works well only for head-on wave incidence. To remedy this, two new elliptic dampers are proposed, one for beam-on incidence and the other for general wave incidence. The performance of all the three dampers is studied using a numerical example of diffraction by an elliptic cylinder. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Hot-electron numerical modelling of short gate length pHEMTs applied to novel field plate structures INTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1 2003Shahzad HussainAbstract Hot-electron numerical simulations were carried out in order to simulate the DC parameters of pseudomorphic high electron mobility transistors (pHEMTs). The hot-electron effects were studied by simulating several HEMT device structures. Hot-carrier injection in the substrate and the formation of the peak of electric field in the channel were studied in detail. The inclusion of a field-plate contact in a multiple recessed pHEMT structure lowered the peak value of the electric field by 24% compared with the conventional pHEMT. These devices were modelled by solving the two-dimensional Poisson, current continuity and energy transport equations consistently with the time-independent Schrödinger wave equation. Appropriate Ohmic boundaries are discussed here and implemented in the simulations of pHEMT structures. A new integral approximation is used to calculate electron densities and electron energy densities for degenerate approximations. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Quasi-static analysis of microstrip lines with variation of substrate thickness in transverse direction INTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2003S. KhouljiAbstract This article is devoted to the analysis of microstrip lines printed on dielectric substrates with transversely varying thickness using the quasi-static approximation and the method of lines. Discretization lines of varying length, according to the layer thickness, are used and only the Laplace wave equation has to be solved. The numerical results presented herein permit the illustration of the effect of arbitrarily curved substrate interfaces along the transverse direction on the characteristics of the microstrip structures under consideration. The behavior of the per unit length parameters of these structures as a function of the shape of these substrates' cross section is studied in depth. Furthermore, the effects of the finite metallization thickness and losses are also investigated in detail. The results that are obtained are consistent with those published in the literature. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 194,205, 2003. [source] ## Hyperfine structure of hydrogen and geonium LASER PHYSICS LETTERS, Issue 2 2004A.V. AndreevAbstract The self-consistent theory of hyperfine atomic structure is developed. The theory is based on Lorentz and gauge invariant equation for action of spin 1/2 particle. The specific feature of proposed equation for action (or Lagrangian) is that it is enable to introduce the three material constants: mass m0, charge q, and magneton (i.e. magnitude of magnetic moment) ,. The analytically tractable solutions of the wave equation for the electron motion in Coulomb field and electron motion in uniform magnetic field are found. In both cases the calculated spectra include the hyperfine splitting that is agreed well with the experimentally observed spectra. The calculated frequencies of 8(12)d3/2 , 8(12)d5/2 transitions in hydrogen atom are compared with the results of experimental measurements by the highprecision spectroscopy methods. It is shown that the results of calculations are in good agreement with the experimentally measured data. (© 2004 by HMS Consultants. Inc. Published exclusively by WILEY-VCH Verlag GmbH & Co.KGaA) [source] ## On compactness of the velocity field in the incompressible limit of the full Navier,Stokes,Fourier system on large domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 10 2009Eduard FeireislAbstract The incompressible limit for the full Navier,Stokes,Fourier system is studied on a family of domains containing balls of the radius growing with a speed that dominates the inverse of the Mach number. It is shown that the velocity field converges strongly to its limit locally in space, in particular, the effect of the sound waves is eliminated by means of the local decay estimates for the acoustic wave equation. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Longtime behavior for a nonlinear wave equation arising in elasto-plastic flow MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2009Yang ZhijianAbstract The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto-plastic flow utt,div{|,u|m,1,u},,,ut+,2u+g(u)=f(x). It proves that under rather mild conditions, the dynamical system associated with above-mentioned IBVP possesses a global attractor, which is connected and has finite Hausdorff and fractal dimension in the phase spaces X1=H(,) × L2(,) and X=(H3(,),H(,)) × H(,), respectively. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Polynomial and analytic stabilization of a wave equation coupled with an Euler,Bernoulli beam MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2009Kaďs AmmariAbstract We consider a stabilization problem for a model arising in the control of noise. We prove that in the case where the control zone does not satisfy the geometric control condition, B.L.R. (see Bardos et al. SIAM J. Control Optim. 1992; 30:1024,1065), we have a polynomial stability result for all regular initial data. Moreover, we give a precise estimate on the analyticity of reachable functions where we have an exponential stability. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Global existence and uniform stability of solutions for a quasilinear viscoelastic problem MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007Salim A. MessaoudiAbstract In this paper the nonlinear viscoelastic wave equation in canonical form with Dirichlet boundary condition is considered. By introducing a new functional and using the potential well method, we show that the damping induced by the viscoelastic term is enough to ensure global existence and uniform decay of solutions provided that the initial data are in some stable set. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Global and exponential attractors for 3-D wave equations with displacement dependent damping MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2006Vittorino PataAbstract A weakly damped wave equation in the three-dimensional (3-D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite-dimensional global and exponential attractors in a slightly weaker topology. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Resonance phenomena in compound cylindrical waveguides MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2006Günter HeinzelmannAbstract We study the large time asymptotics of the solutions u(x,t) of the Dirichlet and the Neumann initial boundary value problem for the wave equation with time-harmonic right-hand side in domains , which are composed of a finite number of disjoint half-cylinders ,1,,,,r with cross-sections ,,1,,,,,r and a bounded part (,compound cylindrical waveguides'). We show that resonances of orders t and t1/2 may occur at a finite or countable discrete set of frequencies ,, while u(x,t) is bounded as t,, for the remaining frequencies. A resonance of order t occurs at , if and only if ,2 is an eigenvalue of the Laplacian ,, in , with regard to the given boundary condition u=0 or ,u/,n=0, respectively. A resonance of order t1/2 occurs at , if and only if (i) ,2 is an eigenvalue of at least one of the Laplacians for the cross-sections ,,1,,,,r, with regard to the respective boundary condition and (ii) the respective homogeneous boundary value problem for the reduced wave equation ,U+,2U=0 in , has non-trivial solutions with suitable asymptotic properties as | x | ,, (,standing waves'). Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Semilinear wave equation with time dependent potential MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2004Nicola ViscigliaAbstract We consider the following semilinear wave equation: (1) for (t,x) , ,t × ,. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption: ,V(t,x),,C(1+t)(1+,x,) for a.e. (t,x) , ,t × , where C, ,0>0 are real constants, then for any real number , that satisfies there exists a real number ,(f,g,,)>0 such that the equation has a global solution provided that 0<,,,(f,g,,). Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Error estimates for mixed finite element approximations of the viscoelasticity wave equation MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2004Liping GaoAbstract This paper studies mixed finite element approximations to the solution of the viscoelasticity wave equation. Two new transformations are introduced and a corresponding system of first-order differential-integral equations is derived. The semi-discrete and full-discrete mixed finite element methods are then proposed for the problem based on the Raviart,Thomas,Nedelec spaces. The optimal error estimates in L2 -norm are obtained for the semi-discrete and full-discrete mixed approximations of the general viscoelasticity wave equation. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Local energy decay for linear wave equations with non-compactly supported initial data MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 16 2004Ryo IkehataAbstract A local energy decay problem is studied to a typical linear wave equation in an exterior domain. For this purpose, we do not assume any compactness of the support on the initial data. This generalizes a previous famous result due to Morawetz (Comm. Pure Appl. Math. 1961; 14:561,568). In order to prove local energy decay we mainly apply two types of new ideas due to Ikehata,Matsuyama (Sci. Math. Japon. 2002; 55:33,42) and Todorova,Yordanov (J. Differential Equations 2001; 174:464). Copyright © 2004 John Wiley & Sons, Ltd. [source] |