Electron. J. Diff. Eqns., Vol. 2002(2002), No. 22, pp. 1-18.

Existence of solutions for a variational unilateral system

Marcondes R. Clark & Osmundo A. Lima

Abstract:
In this work the authors study the existence of weak solutions of the nonlinear unilateral mixed problem associated to the inequalities
$$ \displaylines{ u_{tt}-M(| \nabla u| ^{2})\Delta u+\theta \geq f, \cr \theta_t-\Delta \theta +u_t\geq g ,} $$
where f, g, m are given real-valued functions with M positive.

Submitted November 17, 2000. Published February 21, 2002.
Math Subject Classifications: 35L85, 49A29.
Key Words: weak solutions, variational unilateral nonlinear problem, Galerkin method, penalization method.

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Marcondes R. Clark
Federal University of Piaui - CCN - DM
Av. Ininga S/N - 64.049-550 - Teresina - PI - Brazil
e-mail: mclark@ufpi.br

Osmundo A. Lima
State University of Paraiba-DM
CEP 58.109-095 - Campina Grande - PB- Brazil
e-mail: osmundo@openline.com.br

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