Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach

Paronetto, Fabio

doi:10.1051/cocv:2007029

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Asymptotic behaviour of a class of degenerate elliptic-parabolic operators : a unitary approach

Paronetto, Fabio

ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 669-691

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Résumé

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations $\partial_{t} (r_{h} u) - div (a_{h} \cdot D u)$ with $r_{h} (x, t) \geq 0$ , $r_{h} \in L^{\infty} (Ω \times (0, T))$ . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain $G$ -convergence for elliptic operators $(r_{h} \equiv 0)$ , $G$ -convergence for parabolic operators $(r_{h} \equiv 1)$ , singular perturbations of an elliptic operator $(a_{h} \equiv a$ and $r_{h} \to r$ , possibly $r \equiv 0)$ .

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},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {4},
     year = {2007},
     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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