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

Fabio Paronetto

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 4, page 669-691
  • ISSN: 1292-8119

Abstract

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We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations ∂ t ( r h u ) - div ( a h · D u ) 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 ) .

How to cite

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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 13.4 (2007): 669-691. <http://eudml.org/doc/250006>.

@article{Paronetto2007,
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 $r\equiv 0)$. },
author = {Paronetto, Fabio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {G-convergence; PDE of mixed type; linear elliptic and parabolic equations; -convergence; singular perturbations; lack of compactness},
language = {eng},
month = {7},
number = {4},
pages = {669-691},
publisher = {EDP Sciences},
title = {Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach},
url = {http://eudml.org/doc/250006},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Paronetto, Fabio
TI - Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/7//
PB - EDP Sciences
VL - 13
IS - 4
SP - 669
EP - 691
AB - 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 $r\equiv 0)$.
LA - eng
KW - G-convergence; PDE of mixed type; linear elliptic and parabolic equations; -convergence; singular perturbations; lack of compactness
UR - http://eudml.org/doc/250006
ER -

References

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