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{ . }
Categories: math.AP