Article contents
Asymptotic behaviour of a class of degenerateelliptic-parabolic operators: a unitary approach
Published online by Cambridge University Press: 20 July 2007
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 $r\equiv 0)$
.
- 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
References
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