Stability properties for quasilinear parabolic equations with measure data

Abstract: Let $\Omega$ be a bounded domain of $\mathbb{R}^{N}$, and $Q=\Omega \times(0,T).$ We study problems of the model type [ \left{ \begin{array} [c]{l}% {u_{t}}-{\Delta_{p}}u=\mu\qquad\text{in }Q,\ {u}=0\qquad\text{on }\partial\Omega\times(0,T),\ u(0)=u_{0}\qquad\text{in }\Omega, \end{array} \right. ] where $p>1$, $\mu\in\mathcal{M}{b}(Q)$ and $u{0}\in L^{1}(\Omega).$ Our main result is a \textit{stability theorem }extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u\longmapsto\mathcal{A}(u)=$div$(A(x,t,\nabla u))$\textit{. }