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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
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Abstract

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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