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Asymptotic behaviour of a class of degenerateelliptic-parabolic operators: a unitary approach

Published online by Cambridge University Press:  20 July 2007

Fabio Paronetto
Fabio Paronetto*
Affiliation:
Dipartimento di Matematica “Ennio De Giorgi”, Università del Salento, via per Arnesano, 73100 Lecce, Italy; fabio.paronetto@unile.it
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Abstract

We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations $\partial_t (r_h u) - {\rm div}(a_h \cdot Du)$ with $r_h(x,t) \geq0$, $r_h \in L^{\infty}(\Omega\times (0,T))$. 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 $r\equiv 0)$.

Keywords

G-convergencePDE of mixed typelinear elliptic and parabolic equations
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 4 , October 2007 , pp. 669 - 691
Copyright
© EDP Sciences, SMAI, 2007

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