A singular perturbation problem for nonlinear damped hyperbolic equations-Reference-Cited by-同舟云学术

A singular perturbation problem for nonlinear damped hyperbolic equations

Published:1989 Issue:1-2 Volume:111 Page:21-31
ISSN:0308-2105
Container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics
language:en
Short-container-title:Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Author:

Biler Piotr

Abstract

SynopsisWe consider damped nonlinear hyperbolic equations utt + Aut + αAu + βA2u + G(u) = 0, where A is a positive operator and G is the Gateaux derivative of a convex functional. We examine the asymptotic behaviour of solutions and the convergence of strong solutions to these equations when the parameter β tends to zero.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference6 articles.

1. Convergence properties of the strongly damped nonlinear Klein-Gordon equation

2. Nonlinear second order equations with applications to partial differential equations

3. Remark on the decay for damped string and beam equations

4. Nonlinear initial-boundary value problems

5. Semigroups of Linear Operators and Applications to Partial Differential Equations

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The global solution of an initial boundary value problem for the damped Boussinesq equation;Communications on Pure & Applied Analysis;2004

2. On the spatially two-dimensional Boussinesq equation in a circular domain;Nonlinear Analysis: Theory, Methods & Applications;2001-11

3. Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation;Discrete & Continuous Dynamical Systems - A;2001

4. On the damped Boussinesq equation in a circle;Nonlinear Analysis: Theory, Methods & Applications;1999-11

5. Limiting behaviour of invariant manifolds for a system of singularly perturbed evolution equations;Mathematical Methods in the Applied Sciences;1994-06-25