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Wave Solutions (wave + solution)

Distribution by Scientific Domains

Mathematics and Statistics	81%
Engineering	18%

Kinds of Wave Solutions

traveling wave solution

Selected Abstracts

Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 4 2009
Yoshihiro Ueda
Abstract We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as t,, if the initial disturbance decays polynomially (resp. exponentially) for x,,. Our proofs are based on the space,time weighted energy method. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Multi-dimensional combustion waves for Lewis number close to one

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2007
A. Ducrot
Abstract This paper is devoted to the study of multi-dimensional travelling wave solution for a thermo-diffusive model, describing the propagation of curved flames in an infinite cylinder. The linear dependence of the components of the reaction rate together with the existence of an ignition temperature ensure that the corresponding linearized operator does not satisfy the Fredholm property. A direct consequence is that solvability conditions for the linearized operator are not known and classical methods of nonlinear analysis cannot be directly applied. We prove in this paper existence results of such travelling waves, by first introducing a suitable re-formulation of the equations and then by choosing suitable weighted spaces that allows us to move the essential spectrum away from zero. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Dynamic response of soft poroelastic bed to linear water waves,a boundary layer correction approach

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2001
Ping-Cheng Hsieh
Abstract According to Chen et al. (Journal of Engineering Mechanics, ASCE 1997; 123(10):1041,1049.) a boundary layer exists within the porous bed and near the homogeneous-water/porous-bed interface when oscillatory water waves propagate over a soft poroelastic bed. This boundary layer makes the evaluation of the second kind of longitudinal wave inside the soft poroelastic bed very inaccurate. In this study, the boundary layer correction approach for the poroelastic bed is applied to the boundary value problem of linear oscillatory water waves propagating over a soft poroelastic bed. After the analyses of length scale and order of magnitude of physical variables are done, a perturbation expansion for the boundary layer correction approach based on two small parameters is proposed and solved. The solutions are carried out for the first and third kind of waves throughout the entire domain. The second kind of wave which disappears outside the boundary layer is solved systematically inside the boundary layer. The results are compared with the linear wave solutions of Huang and Song (Journal of Engineering Mechanics, ASCE 1993; 119:1003,1020.) to confirm the validity. Moreover, a simplified boundary layer correction formulation which is expected to be very useful in numerical computation is also proposed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Quasi optimal finite difference method for Helmholtz problem on unstructured grids

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2010
Daniel T. Fernandes
Abstract A quasi optimal finite difference method (QOFD) is proposed for the Helmholtz problem. The stencils' coefficients are obtained numerically by minimizing a least-squares functional of the local truncation error for plane wave solutions in any direction. In one dimension this approach leads to a nodally exact scheme, with no truncation error, for uniform or non-uniform meshes. In two dimensions, when applied to a uniform cartesian grid, a 9-point sixth-order scheme is derived with the same truncation error of the quasi-stabilized finite element method (QSFEM) introduced by Babu,ka et al. (Comp. Meth. Appl. Mech. Eng. 1995; 128:325,359). Similarly, a 27-point sixth-order stencil is derived in three dimensions. The QOFD formulation, proposed here, is naturally applied on uniform, non-uniform and unstructured meshes in any dimension. Numerical results are presented showing optimal rates of convergence and reduced pollution effects for large values of the wave number. Copyright © 2009 John Wiley & Sons, Ltd. [source]

Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation

Existence of periodic traveling wave solutions for the Ostrovsky equation

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2008
Naoyuki Ishimura
Abstract We are concerned with the Ostrovsky equation, which is derived from the theory of weakly nonlinear long surface and internal waves in shallow water under the presence of rotation. On the basis of the variational method, we show the existence of periodic traveling wave solutions. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Shock formation in a chemotaxis model

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 1 2008
Zhian Wang
Abstract In this paper, we establish the existence of shock solutions for a simplified version of the Othmer,Stevens chemotaxis model (SIAM J. Appl. Math. 1997; 57:1044,1081). The existence of these shock solutions was suggested by Levine and Sleeman (SIAM J. Appl. Math. 1997; 57:683,730). Here, we consider the general Riemann problem and derive the shock curves in parameterized forms. By studying the travelling wave solutions, we examine the shock structure for the chemotaxis model and prove that the travelling wave speed is identical to the shock speed. Moreover, we explicitly derive an entropy,entropy flux pair to prove the uniqueness of the weak shock solutions. Some discussion is given for further study. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Delta and singular delta locus for one-dimensional systems of conservation laws

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 8 2004
Marko Nedeljkov
Abstract This work gives a condition for existence of singular and delta shock wave solutions to Riemann problem for 2×2 systems of conservation laws. For a fixed left-hand side value of Riemann data, the condition obtained in the paper describes a set of possible right-hand side values. The procedure is similar to the standard one of finding the Hugoniot locus. Fluxes of the considered systems are globally Lipschitz with respect to one of the dependent variables. The association in a Colombeau-type algebra is used as a solution concept. Copyright © 2004 John Wiley &Sons, Ltd. [source]

Linear vs. nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 5 2004
Marcello Lucia
We revisit the classical problem of speed selection for the propagation of disturbances in scalar reaction-diffusion equations with one linearly stable and one linearly unstable equilibrium. For a wide class of initial data this problem reduces to finding the minimal speed of the monotone traveling wave solutions connecting these two equilibria in one space dimension. We introduce a variational characterization of these traveling wave solutions and give a necessary and sufficient condition for linear versus nonlinear selection mechanism. We obtain sufficient conditions for the linear and nonlinear selection mechanisms that are easily verifiable. Our method also allows us to obtain efficient lower and upper bounds for the propagation speed. © 2004 Wiley Periodicals, Inc. [source]