Asymptotic behaviour of a class of elliptic-parabolic operators: a unified approach

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations partial derivative t(r(h)u) - div(a(h).Du) with r(h)(x, t) >= 0, r(h) is an element of L-infinity (Omega x( 0, T)). The main problem is the lack of compactness, by- passed via a regularity result. As particular cases, we obtain G- convergence for elliptic operators (r(h) equivalent to 0), G-convergence for parabolic operators (r(h) equivalent to 1), singular perturbations of an elliptic operator (a(h) equivalent to a and r(h)-> r, possibly r equivalent to 0).