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 \[ \left\{ \begin{array} [c]{l}% {u_{t}}-{Δ_{p}}u=μ\qquad\text{in }Q,\\ {u}=0\qquad\text{on }\partialΩ\times(0,T),\\ u(0)=u_{0}\qquad\text{in }Ω, \end{array} \right. \] 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 $u⟼\mathcal{A}(u)=$div$(A(x,t,\nabla u))$\textit{. }

arXiv admin note: substantial text overlap with arXiv:1310.5253