Title: Energy decay to the Cauchy problem for a generalised nonlinear Klein-Gordon equation with a nonlinear dissipative term

Authors: Mitsuhiro Nakao

Addresses: Faculty of Mathematics, Kyushu University, Moto-oka 819-0395, Fukuoka, Japan

Abstract: We derive a precise decay rate of energy of solutions to the Cauchy problem for the wave equation with a nonlinear dissipative term and an absorbing term. Due to the absorbing term the equation is regarded as a generalised Klein-Gordon equation with a nonlinear dissipative term. This observation plays an important role in the proof.

Keywords: energy decay; wave equations; nonlinear dissipation terms; Cauchy problem; generalised Klein-Gordon equations; decay rate; absorbing terms.

DOI: 10.1504/IJDSDE.2011.041880

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.3, pp.349 - 362

Published online: 24 Jan 2015 *

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