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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 561-570

Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain

Departamento de Matemática, Instituto Tecnológico de Aeronáutica, Centro Técnico Aeroespacial, São José dos Campos 12228-900, SP, Brazil

Received 9 January 1992; Revised 10 October 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we study the existence of solutions of the following nonlinear hyperbolic svstem|u+A(t)u+b(x)G(u)=finQu=0onΣu(0)=uοu1(0)=u1where Q is a noncylindrical domain of n+1 with lateral boundary Σ, u(u1,u2) a vector defined on Q, {A(t),0t+} is a family of operators in (Hο1(Ω),H1(Ω)), where A(t)u=(A(t)u1,A(t)u2) and G:22 a continuous function such that x.G(x)0, for x2.

Moreover, we obtain that the solutions of the above system with dissipative term u have exponential decay.