Geodesic
Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 669-691
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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 r≡0).

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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     title = {Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {669--691},
     year = {2007},
     publisher = {EDP-Sciences},
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     number = {4},
     doi = {10.1051/cocv:2007029},
     mrnumber = {2351397},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007029/}
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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, Tome 13 (2007) no. 4, pp. 669-691. doi: 10.1051/cocv:2007029

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