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

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

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 (sfgeng@xtu.edu.cn)
Lina Zhang
Affiliation:
School of Mathematics and Computational Science, Xiangtan University, Hunan 411105, People’s Republic of China (zln514@163.com) and School of Mathematics and Statistics, Central South University, Changsha 410075, People’s Republic of China
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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 

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