Electron. J. Diff. Eqns., Vol. 1997(1997), No. 06, pp 1-11.

On a mixed problem for a coupled nonlinear system

M. R. Clark & O. A. Lima

Abstract:
In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system
$$\eqalign{ u_{tt}-M(\int_\Omega |\nabla u|^2dx)\Delta u+|u|^\rho u+\theta &=f \cr \theta _t -\Delta \theta +u_{t}&=g \cr} $$
where M is a positive real function, and f and g are known real functions.

Submitted November 26, 1996. Published March 6, 1997.
Math Subject Classification: 35M10.
Key Words: Mixed problem, nonlinear system, weak solutions, uniqueness.

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M. R. Clark
Universidade Federal da Paraiba PB, Brasil
e-mail: mclark@dme.ufpb.br

O. A. Lima
Universidade Estadual da Paraiba DM, Brasil
e-mail: olima@dme.ufpb.br

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