Existence and Uniqueness Results for Quasilinear Parabolic Systems in Orlicz Spaces

Abstract

We establish an existence and uniqueness result for quasilinear parabolic systems of the form $\frac {\partial u}{\partial t}-\text {div} \sigma (x,t,Du)=f$ in Q, where the source term f is assumed to be in $W^{-1,x}E_{\overline {M}}(Q;\mathbb {R}^{m})$. The proof is based on the theory of Young measures which permits to identify weak limits.