On a mixed problem for a coupled nonlinear system

Abstract

In this article we prove the existence and uniqueness of solutions to the mixed problem associated with the nonlinear system $$ u_{tt}-M(int_Omega |abla u|^2dx)Delta u+|u|^ ho u+heta =f $$ $$ heta _t -Delta heta +u_{t}=g $$ where $M$ is a positive real function, and $f$ and $g$ are known real functions.

Keywords

• Mixed problem
• nonlinear system
• weak solutions
• uniqueness.