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

where $p>1$, $\mu \in {\mathcal{M}}_b(Q)$ and $u_0\in L^1(\Omega ).$ Our main result is a stability theorem extending the results of Dal Maso, Murat, Orsina, Prignet, for the elliptic case, valid for quasilinear operators $u⟼\mathcal{A}(u)=$div$(A(x,t,\nabla u))$.