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Asymptotic behaviour of a class of degenerateelliptic-parabolic operators: a unitary approach
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- Journal:
- ESAIM: Control, Optimisation and Calculus of Variations / Volume 13 / Issue 4 / October 2007
- Published online by Cambridge University Press:
- 20 July 2007, pp. 669-691
- Print publication:
- October 2007
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- Article
- Export citation
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We study the asymptotic behaviour of a sequence of stronglydegenerate 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 perturbationsof an elliptic operator $(a_h \equiv a$ 
and $r_h \to r$ 
, possibly $r\equiv 0)$ 
.
