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

Shifeng Geng; Lina Zhang

doi:10.1017/S0308210515000219

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

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

Published online by Cambridge University Press: 26 August 2015

Shifeng Geng and

Lina Zhang

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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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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.