Existence of solutions for a variational unilateral system

Abstract

In this work the authors study the existence of weak solutions of the nonlinear unilateral mixed problem associated to the inequalities $$ displaylines{ u_{tt}-M(| abla u| ^{2})Delta u+heta geq f, cr heta_t-Delta heta +u_tgeq g ,} $$ where $f$, $g$, $M$ are given real-valued functions with $M$ positive.

Keywords

• weak solutions
• variational unilateral nonlinear problem
• Galerkin method
• penalization method.