Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2014; 51(6): 1697-1710

Printed November 30, 2014

https://doi.org/10.4134/BKMS.2014.51.6.1697

Copyright © The Korean Mathematical Society.

Global existence and nonexistence of solutions for coupled nonlinear wave equations with damping and source terms

Yaojun Ye

Zhejiang University of Science and Technology

Abstract

The initial-boundary value problem for a class of nonlinear higher-order wave equations system with a damping and source terms in bounded domain is studied. We prove the existence of global solutions. Meanwhile, under the condition of the positive initial energy, it is showed that the solutions blow up in the finite time and the lifespan estimate of solutions is also given.

Keywords: systems of nonlinear wave equations, damping and source terms, global solutions, blow-up, lifespan of solutions

MSC numbers: 35G50, 35L55, 35L05