Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach
ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 669-691.

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations t (r h u)- 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 r0).

DOI: 10.1051/cocv:2007029
Classification: 35J15, 35K10, 35M10, 45J45
Keywords: $G$-convergence, PDE of mixed type, linear elliptic and parabolic equations
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Paronetto, Fabio. Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach. ESAIM: Control, Optimisation and Calculus of Variations, Volume 13 (2007) no. 4, pp. 669-691. doi : 10.1051/cocv:2007029. http://www.numdam.org/articles/10.1051/cocv:2007029/

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