Stability properties for quasilinear parabolic equations with measure data
Marie‐Françoise Bidaut‐Véron, Quoc‐Hung Nguyen · Journal of the European Mathematical Society · 2015
Let \Omega be a bounded domain of \mathbb{R}^{N} , and Q=\Omega \times(0,T). We study problems of the model type \begin{cases} u_t-\Delta_pu=\mu\qquad&\text{in }Q,\\ u=0\qquad &\text{on }\partial\Omega\times(0,T),\\ u(0)=u_0\qquad&\text{in }\Omega, \end{cases} 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\longmapsto\mathcal{A}(u)= div (A(x,t, abla u)) .