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## Asymptotic Behaviour (asymptotic + behaviour)
## Selected Abstracts## Asymptotic behaviour for a two-dimensional thermoelastic model MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2007M. FabrizioAbstract In this paper we study a thermoelastic material with an internal structure which binds the materials fibres to a quadratic behaviour. Moreover, a hereditary constitutive law for heat flux is supposed. We prove results of asymptotic stability and exponential decay for the evolution problem in two-dimensional space domain. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Asymptotic behaviour of solutions of quasilinear evolutionary partial differential equations of parabolic type on unbounded spatial intervals MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2006PoulAbstract We study the long-time behaviour of solutions to a quasilinear parabolic problem on a half-line. The main result lies in showing the existence of a positive solution that converges to the travelling wave of solution to the stationary problem on the whole line. The main tools used here are the zero number theory and the concentration compactness principle. This result is a generalization of a result know for semilinear parabolic equations. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Asymptotic behaviour of global smooth solutionsto the multidimensional hydrodynamic model for semiconductors MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2002Ling HsiaoAbstract In this paper, we study asymptotic behaviour of the global smooth solutions to the multidimensional hydrodynamic model for semiconductors. We prove that the solution of the problem converges to a stationary solution time asymptotically exponentially fast. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Asymptotic behaviour for a non-monotone fluid in one dimension: the positive temperature case MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2001B. DucometWe consider a one-dimensional continuous model of neutron star, described by a compressible Navier,Stokes system with a non-monotone equation of state, due to the effective Skyrme nuclear interaction between particles. We study the asymptotic behaviour of globally defined solutions of a mixed free boundary problem for our model, for large time, assuming that a sufficient thermal dissipation is present. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Asymptotic behaviour of the finite-time ruin probability in renewal risk models APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009Remigijus LeipusAbstract In this paper we study the tail behaviour of the probability of ruin within finite time t, as initial risk reserve x tends to infinity, for the renewal risk model with strongly subexponential claim sizes. The asymptotic formula holds uniformly for t,[f(x), ,), where f(x) is an infinitely increasing function, and substantially extends the result of Tang (Stoch. Models 2004; 20:281,297) obtained for the class of claim distributions with consistently varying tails. Two examples illustrate the result. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Vectorial summation of probabilistic current harmonics in power systems: From a bivariate distribution model towards a univariate probability function EUROPEAN TRANSACTIONS ON ELECTRICAL POWER, Issue 1 2000Y. J. WangThis paper extends the investigation into the bivariate normal distribution (BND) model which has been widely used to study the asymptotic behaviour of the sum of a sufficiently large number of randomly-varying harmonic phasors (of the same frequency). Although the BND model is effective and applicable to most problems involving harmonic summation, its main drawback resides in the computation time required to extract the probability density function of the harmonic magnitude from the two-dimensional BND model. This paper proposes a novel approach to the problem by assimilating the generalized Gamma distribution (GGD) model to the marginal distribution (the magnitude) of the BND using the method of moments. The proposed method can accurately estimate the parameters of the GGD model without time-consuming calculation. A power system containing ten harmonic sources is taken as an example where the comparison of the Monte-Carlo simulation, the BND model and the GGD model is given and discussed. The comparison shows that the GGD model approximates the BND model very well. [source] ## Generalization of robustness test procedure for error estimators. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2005Part I: formulation for patches near kinked boundariesAbstract In this part of paper we shall extend the formulation proposed by Babu,ka and co-workers for robustness patch test, for quality assessment of error estimators, to more general cases of patch locations especially in three-dimensional problems. This is performed first by finding an asymptotic finite element solution at interior parts of a problem with assumed smooth exact solution and then adding a correction part to obtain the solution near a kinked boundary irrespective of other boundary conditions at far ends of the domain. It has been shown that the solution corresponding to the correction part may be obtained in a spectral form by assuming a suitable proportionality relation between the nodal values of a mesh with repeatable pattern of macro-patches. Having found the asymptotic finite element solution, the performance of error estimators may be examined. Although in this paper we focus on the asymptotic behaviour of error estimators, the method described in this part may be used to obtain finite element solution for two/three-dimensional unbounded heat/elasticity problems with homogeneous differential equations. Some numerical results are presented to show the validity and performance of the proposed method. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Improvement of the asymptotic behaviour of the Euler,Maclaurin formula for Cauchy principal value and Hadamard finite-part integrals INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004U. Jin ChoiAbstract In the recent works (Commun. Numer. Meth. Engng 2001; 17: 881; to appear), the superiority of the non-linear transformations containing a real parameter b , 0 has been demonstrated in numerical evaluation of weakly singular integrals. Based on these transformations, we define a so-called parametric sigmoidal transformation and employ it to evaluate the Cauchy principal value and Hadamard finite-part integrals by using the Euler,Maclaurin formula. Better approximation is expected due to the prominent properties of the parametric sigmoidal transformation of whose local behaviour near x = 0 is governed by parameter b. Through the asymptotic error analysis of the Euler,Maclaurin formula using the parametric sigmoidal transformation, we can observe that it provides a distinct improvement on its predecessors using traditional sigmoidal transformations. Numerical results of some examples show the availability of the present method. Copyright © 2004 John Wiley & Sons, Ltd. [source] ## Development of an optimal hybrid finite volume/element method for viscoelastic flows INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2003M. AboubacarAbstract A cell-vertex hybrid finite volume/element method is investigated that is implemented on triangles and applied to the numerical solution of Oldroyd model fluids in contraction flows. Particular attention is paid to establishing high-order accuracy, whilst retaining favourable stability properties. Elevated levels of elasticity are sought. The main impact of this study reveals that switching from quadratic to linear finite volume stress representation with discontinuous stress gradients, and incorporating local reduced quadrature at the re-entrant corner, provide enhance stability properties. Solution smoothness is achieved by adopting the non-conservative flux form with area integration, by appealing to quadratic recovered velocity-gradients, and through consistency considerations in the treatment of the time term in the constitutive equation. In this manner, high-order accuracy is maintained, stability is ensured, and the finer features of the flow are confirmed via mesh refinement. Lip vortices are observed for We>1, and a trailing-edge vortex is also apparent. Loss of evolution and solution asymptotic behaviour towards the re-entrant corner are also discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## A test of homogeneity for autoregressive processes INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 3 2002Rafael Martínez Pedro GómezAbstract In this paper, we introduce a new hypothesis test to determine whether or not two spectral densities are proportional. We deliberately limit our study to autoregressive processes and derive the asymptotic behaviour of the test. A test for autoregressive coefficient nullity or randomness is deduced. We derive asymptotic behaviour for these tests and show the usefulness of our test to detect speech in a noisy environment. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Finite sample improvements in statistical inference with I(1) processes JOURNAL OF APPLIED ECONOMETRICS, Issue 3 2001D. MarinucciRobinson and Marinucci (1998) investigated the asymptotic behaviour of a narrow-band semiparametric procedure termed Frequency Domain Least Squares (FDLS) in the broad context of fractional cointegration analysis. Here we restrict discussion to the standard case when the data are I(1) and the cointegrating errors are I(0), proving that modifications of the Fully Modified Ordinary Least Squares (FM-OLS) procedure of Phillips and Hansen (1990) which use the FDLS idea have the same asymptotically desirable properties as FM-OLS, and, on the basis of a Monte Carlo study, find evidence that they have superior finite-sample properties. The new procedures are also shown to compare satisfactorily with parametric estimates. Copyright © 2001 John Wiley & Sons, Ltd. [source] ## Autoregressive processes with data-driven regime switching JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2009Joseph Tadjuidje KamgaingAbstract., We develop a switching-regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process. In contrast to the typical hidden Markov approach, we allow the transition probabilities of the underlying Markov process to depend on past values of the time series and exogenous variables. Such processes have potential applications in finance and neuroscience. In the latter, the brain activity at time t (measured by electroencephalograms) will be modelled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). In this article, we establish stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behaviour of various statistics and model parameter estimators. [source] ## On residual empirical processes of GARCH-SM models: application to conditional symmetry tests JOURNAL OF TIME SERIES ANALYSIS, Issue 5 2008Naâmane Laďb62M10; 62G10 Abstract., Considering the generalized autoregressive conditionally heteroskedastic with stochastic mean (GARCH-SM) model, we establish in this article the consistency and the weak representation of a functional of its residual empirical process. Based on this result, a symmetry test for GARCH-SM model is developed. Simulations are given to show the asymptotic behaviour and normality of the test statistic. [source] ## Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein,Gordon equation with dissipative term MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2010Xu RunzhangAbstract We study the Cauchy problem of nonlinear Klein,Gordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a sharp condition for global existence and finite time blow up of solutions. Copyright © 2009 John Wiley & Sons, Ltd. [source] ## The asymptotic behaviour of weak solutions to the forward problem of electrical impedance tomography on unbounded three-dimensional domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2009Michael LukaschewitschAbstract The forward problem of electrical impedance tomography on unbounded domains can be studied by introducing appropriate function spaces for this setting. In this paper we derive the point-wise asymptotic behaviour of weak solutions to this problem in the three-dimensional case. Copyright © 2008 John Wiley & Sons, Ltd. [source] ## Homogenization of elliptic problems with the Dirichlet and Neumann conditions imposed on varying subsets MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2007Carmen Calvo-JuradoAbstract We study the asymptotic behaviour of the solution un of a linear elliptic equation posed in a fixed domain ,. The solution un is assumed to satisfy a Dirichlet boundary condition on ,n, where ,n is an arbitrary sequence of subsets of ,,, and a Neumman boundary condition on the remainder of ,,. We obtain a representation of the limit problem which is stable by homogenization and where it appears a generalized Fourier boundary condition. We also prove a corrector result. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## On the asymptotic stability of steady solutions of the Navier,Stokes equations in unbounded domains MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2007Francesca CrispoAbstract We consider the problem of the asymptotic behaviour in the L2 -norm of solutions of the Navier,Stokes equations. We consider perturbations to the rest state and to stationary motions. In both cases we study the initial-boundary value problem in unbounded domains with non-compact boundary. In particular, we deal with domains with varying and possibly divergent exits to infinity and aperture domains. Copyright © 2007 John Wiley & Sons, Ltd. [source] ## Dynamic and generalized Wentzell node conditions for network equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2007Delio MugnoloAbstract Motivated by a neurobiological problem, we discuss a class of diffusion problems on a network. The celebrated Rall lumped soma model for the spread of electrical potential in a dendritical tree prescribes that the common cable equation must be coupled with particular dynamic conditions in some nodes (the cell bodies, or somata). We discuss the extension of this model to the case of a whole network of neurons, where the ramification nodes can be either active (with excitatory time-dependent boundary conditions) or passive (where no dynamics take place, i.e. only Kirchhoff laws are imposed). While well-posedness of the system has already been obtained in previous works, using abstract tools based on variational methods and semigroup theory we are able to prove several qualitative properties, including asymptotic behaviour, regularity of solutions, and monotonicity of the semigroups in dependence on the physical coefficients. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Local existence for the one-dimensional Vlasov,Poisson system with infinite mass MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2007Stephen PankavichAbstract A collisionless plasma is modelled by the Vlasov,Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as ,x, , ,. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Asymptotic analysis of elastic curved rods MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2007Rostislav VodákAbstract We consider a sequence of curved rods which consist of isotropic material and which are clamped on the lower base or on both bases. We study the asymptotic behaviour of the stress tensor and displacement under the assumptions of linearized elasticity when the cross-sectional diameter of the rods tends to zero and the body force is given in the particular form. The analysis covers the case of a non-smooth limit line of centroids. We show how the body force and the choice of the approximating curved rods can affect the strong convergence and the limit form of the stress tensor for the curved rods clamped on both bases. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## Convergence of phase field to phase relaxation models governed by an entropy equation with memory MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2006Gianni GilardiAbstract The subject of the present paper consists in proving the convergence of a phase-field model, based on the entropy equation with memory, to phase relaxation. The well-posedness and the long-time behaviour of solutions for the non-linear and singular phase-field system have been recently shown by Bonetti et al. (Preprint IMATI-CNR, 2005; Discrete Contin. Dyn. Syst. Ser. B, in press). Here, we study the asymptotic behaviour of such solutions as the interfacial energy coefficient tends to zero. The limit problem is a phase relaxation problem with memory, which is new. We prove well-posedness results through convergence under rather general assumptions. However, the case of a quadratic non-linearity for the latent heat is excluded. Such a situation is dealt for the problem without memory in a generalized setting by introducing an ad hoc logarithm. Copyright © 2006 John Wiley & Sons, Ltd. [source] ## On the asymptotic behaviour of the discrete spectrum in buckling problems for thin plates MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2006Monique DaugeAbstract We consider the buckling problem for a family of thin plates with thickness parameter ,. This involves finding the least positive multiple , of the load that makes the plate buckle, a value that can be expressed in terms of an eigenvalue problem involving a non-compact operator. We show that under certain assumptions on the load, we have , = ,,(,2). This guarantees that provided the plate is thin enough, this minimum value can be numerically approximated without the spectral pollution that is possible due to the presence of the non-compact operator. We provide numerical computations illustrating some of our theoretical results. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Some remarks on the asymptotic behaviour of the solutions of a class of parabolic problems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2006G. A. PhilippinAbstract This paper deals with a class of semilinear parabolic problems. We establish sufficient conditions on the data forcing the solution to blow up at finite time , and derive an upper bound for ,. Moreover, we show that if the problem is modified in some way, the solution decays exponentially in time and depends continuously on the data. Copyright © 2005 John Wiley & Sons, Ltd. [source] ## Initial boundary value problem for a class of non-linear strongly damped wave equations MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2003Yang ZhijianThe paper studies the existence, asymptotic behaviour and stability of global solutions to the initial boundary value problem for a class of strongly damped non-linear wave equations. By a H00.5ptk-Galerkin approximation scheme, it proves that the above-mentioned problem admits a unique classical solution depending continuously on initial data and decaying to zero as t,+,as long as the non-linear terms are sufficiently smooth; they, as well as their derivatives or partial derivatives, are of polynomial growth order and the initial energy is properly small. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## Global and blow-up solutions for non-linear degenerate parabolic systems MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 7 2003Zhi-wen DuanAbstract In this paper the degenerate parabolic system ut=u(uxx+av). vt=v(vxx+bu) with Dirichlet boundary condition is studied. For , the global existence and the asymptotic behaviour (,1=,2) of solution are analysed. For , the blow-up time, blow-up rate and blow-up set of blow-up solution are estimated and the asymptotic behaviour of solution near the blow-up time is discussed by using the ,energy' method. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## The elastic echo problem MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2003Mongi MabroukAbstract We consider a homogeneous isotropic unbounded linear elastic medium ,,,3, having a free boundary ,. A forcing f(t,x) creates an incident displacement field u0(t,x). This primary field is scattered by , giving rise to a secondary field or echo, for which we determine the asymptotic behaviour in time. These results are obtained via the use of an tension of the time-dependent scattering theory of C. Wilcox. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## On the vibrations of a plate with a concentrated mass and very small thickness MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2003D. GómezAbstract We consider the vibrations of an elastic plate that contains a small region whose size depends on a small parameter ,. The density is of order O(,,m) in the small region, the concentrated mass, and it is of order O(1) outside; m is a positive parameter. The thickness plate h being fixed, we describe the asymptotic behaviour, as ,,O, of the eigenvalues and eigenfunctions of the corresponding spectral problem, depending on the value of m: Low- and high-frequency vibrations are studied for m>2. We also consider the case where the thickness plate h depends on ,; then, different values of m are singled out. Copyright © 2003 John Wiley & Sons, Ltd. [source] ## On singular mono-energetic transport equations in slab geometry MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2002Mohamed ChabiIn this paper we establish the well posedness of the Cauchy problem associated to transport equations with singular cross-sections (i.e. unbounded collisions frequencies and unbounded collision operators) in L1 spaces for specular reflecting boundary conditions. In addition, we discuss the weak compactness of the second-order remainder term of the Dyson,Phillips expansion. This allows us to estimate the essential type of the transport semigroup from which the asymptotic behaviour of the solution is derived. The case of singular transport equations with periodic boundary conditions is also discussed. The proofs make use of the Miyadera perturbation theory of positive semigroups on AL -spaces. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Some existence results for conservation laws with source-term MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2002Joăo-Paulo DiasWe prove some new results concerning the existence and asymptotic behaviour of entropy solutions of hyperbolic conservation laws containing non-smooth source-terms. Copyright © 2002 John Wiley & Sons, Ltd. [source] ## Asymptotic behaviour of global smooth solutionsto the multidimensional hydrodynamic model for semiconductors MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2002Ling HsiaoAbstract In this paper, we study asymptotic behaviour of the global smooth solutions to the multidimensional hydrodynamic model for semiconductors. We prove that the solution of the problem converges to a stationary solution time asymptotically exponentially fast. Copyright © 2002 John Wiley & Sons, Ltd. [source] |