Strongly Quasilinear Parabolic Systems in Divergence Form with Weak Monotonicity

Abstract

The existence of solutions to the strongly quasilinear parabolic system<br />[frac{partial u}{partial t}-text{div},sigma(x,t,u,Du)+g(x,t,u,Du)=f,]<br />is proved, where the source term $f$ is assumed to belong to $L^{p'}(0,T; W^{-1,p'}(Omega;R^m))$. Further, we prove the existence of a weak solution by means of the Young measures under mild monotonicity assumptions on $sigma$.