Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-09T06:13:34.968Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary effects and large-time behaviour for quasilinear equations with nonlinear damping

Part of: Hyperbolic equations and systems Materials of strain-rate type and history type, other materials with memory Partial differential equations

Published online by Cambridge University Press:  26 August 2015

Shifeng Geng  and
Lina Zhang
Shifeng Geng
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, People’s Republic of China ([email protected])
Lina Zhang
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, People’s Republic of China ([email protected]) and School of Mathematics and Statistics, Central South University, Changsha 410075, People’s Republic of China
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is concerned with the asymptotic behaviour of solutions to quasilinear hyperbolic equations with nonlinear damping on the quarter-plane (x, t) ∈ ℝ+ x ∈ ℝ+. We obtain the Lp (1 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.

Keywords

convergence ratesboundary effectnonlinear diffusion wavesquasilinear equations

MSC classification

Primary: 35B40: Asymptotic behavior of solutions
Secondary: 35L50: Initial-boundary value problems for first-order hyperbolic systems 35L60: Nonlinear first-order hyperbolic equations 74D10: Nonlinear constitutive equations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 145 , Issue 5 , October 2015 , pp. 959 - 978
Copyright
Copyright © Royal Society of Edinburgh 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)