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Uniform exponential dichotomy and continuity of attractors for singularly perturbed damped wave equations
(Springer, 2006-07-01)
For eta >= 0, we consider a family of damped wave equations u(u) + eta Lambda 1/2u(t) + au(t) + Lambda u = f(u), t > 0, x is an element of Omega subset of R-N, where -Lambda denotes the Laplacian with zero Dirichlet boundary ...
Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations
(Physical Society Japan, 2002-11-01)
Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film ...
Exact boundary control for the wave equation in a polyhedral time-dependent domain
(Elsevier B.V., 1999-05-01)
We establish exact boundary controllability for the wave equation in a polyhedral domain where a part of the boundary moves slowly with constant speed in a small interval of time. The control on the moving part of the ...
On certain new exact solutions of a diffusive predator-prey system
(2013-05-01)
We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the ...
Evolution equation for short surface waves on water of finite depth
(Elsevier B.V., 2009-08-15)
We address the question of determining the evolution equation for surface waves propagating in water whose depth is much larger than the typical wavelength of the surface disturbance. We avoid making the usual approximation ...
Exponential decay for Kirchhoff wave equation with nonlocal condition in a noncylindrical domain
(Elsevier B.V., 2004-06-01)
In this paper, we prove the exponential decay as time goes to infinity of regular solutions of the problem for the Kirchhoff wave equation with nonlocal condition and weak dampingu(tt) - M (\\delU\\(2)(2)) Deltau + ...
A note on the controllability for the wave equation in nonsmooth plane domains
(Elsevier B.V., 2006-01-01)
We study exact boundary controllability for a two-dimensional wave equation in a region which is an angular sector of a circle or an angular sector of an annular region. The control, of Neumann type, acts on the curved ...
On exact boundary controllability for linearly coupled wave equations
(Academic Press Inc. Elsevier B.V., 2011-09-15)
In this paper we study exact boundary controllability for a system of two linear wave equations coupled by lower order terms. We obtain square integrable control of Neuman type for initial state with finite energy, in ...
Stable two-dimensional dispersion-managed soliton
(2003-12-01)
The existence of a dispersion-managed soliton in two-dimensional nonlinear Schrodinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained ...
Disturbance and repair of solitary waves in blood vessels with aneurysm
(Elsevier B.V., 2009-01-01)
This paper analyzes the effects of a local increase of radius followed by local variation of the thickness or rigidity of an elastic tube on the behavior of solitary waves. The basic equations for the analysis is a set of ...