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International Journal of Mathematics and Mathematical Sciences
Volume 11, Issue 2, Pages 335-342
http://dx.doi.org/10.1155/S0161171288000390

On a nonolinear wave equation in unbounded domains

Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, Rio de JaJeiro, RJ CEP 21944, Brazil

Received 16 October 1986

Copyright © 1988 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.

Abstract

We study existence and uniqeness of the nonlinear wave equation2ut2+M(x,|u(x,t)|2dx+|u(x,t)|2dx)(Δu+u)=0in unbounded domains. The above model describes nonlinear wave phenomenon in non-homogeneous media. Our techniques ivolve fixed point arguments combined with the energy method.