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

Published online by Cambridge University Press:  26 August 2015

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
Corresponding

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.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

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