Stability properties for quasilinear parabolic equations with measure data

Let Omega be a bounded domain in R-N, and Q = Omega x (0, T). We study problems of the model type {u(t) - Delta(p)u = mu in Q, u = 0 on partial derivative Omega x (0, T), u(0) = u(0) in Omega, where p > 1, mu is an element of M-b(Q) and u(0) is an element of L-1 (Omega). Our main result is a stability theorem extending the results of Dal Maso, Murat, Orsina and Prignet for the elliptic case, valid for quasilinear operators u bar right arrow A(u) = div(A(x, t, del u)).