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Global non-existence of solutions of a class of wave equations with non-linear damping and source terms

✍ Scribed by Salim A. Messaoudi; Belkacem Said Houari

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
98 KB
Volume
27
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

In this paper we consider the non‐linear wave equation
a,b>0, associated with initial and Dirichlet boundary conditions. We prove, under suitable conditions on α,β,m,p and for negative initial energy, a global non‐existence theorem. This improves a result by Yang (Math. Meth. Appl. Sci. 2002; 25:825–833), who requires that the initial energy be sufficiently negative and relates the global non‐existence of solutions to the size of Ω. Copyright © 2004 John Wiley & Sons, Ltd.

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