ASYMPTOTIC BEHAVIOUR OF A CLASS OF DEGENERATE ELLIPTIC-PARABOLIC OPERATORS: A UNITARY APPROACH

摘要

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations partial deriv_t(r_hu) - div(a_h · Du) with r_h(x,t) ≥ 0, r_h ∈ L~∞(Ω × (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 ≡ 0), G-convergence for parabolic operators (r_h ≡1), singular perturbations of an elliptic operator (a_h ≡ a and r_h→ r, possibly r ≡ 0).