On the existence of solutions for a strongly degenerate system

María Teresa González Montesinos; Francisco Ortegón Gallego

doi:10.1016/j.crma.2006.06.002

Partial Differential Equations

On the existence of solutions for a strongly degenerate system
[Sur l'existence de solutions pour un système fortement dégénéré]

Présenté par : Olivier Pironneau

María Teresa González Montesinos ¹ ; Francisco Ortegón Gallego ²

¹ Departamento de Matemáticas, Universidad de Cádiz, Facultad de Ciencias Empresariales, 11002 Cádiz, Spain
² Departamento de Matemáticas, Universidad de Cádiz, CASEM, Campus del Río San Pedro, 11510 Puerto Real, Spain

Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 119-123.

Résumé
Abstract

On montre l'existence d'une solution dans un certain sens d'un problème fortement dégénéré constitué par un système non-linéaire de deux équations aux dérivées partielles couplées du type parabolique-elliptique, le terme de diffusion de l'équation parabolique étant de la forme $- div a (x, t, u, \nabla u)$ , où a est un opérateur du type de Leray–Lions. En outre, la seconde équation de ce système est non-uniformement elliptique.

We establish the existence of a solution in a certain sense to a strongly degenerate problem consisting in a coupled nonlinear parabolic-elliptic system. The diffusion term in the parabolic equation is of the form $- div a (x, t, u, \nabla u)$ , where a is an operator of the Leray–Lions type. Moreover, the second equation is nonuniformly elliptic.

Reçu le : 2006-02-20
Accepté le : 2006-06-01
Publié le : 2006-07-11

DOI : 10.1016/j.crma.2006.06.002

Affiliations des auteurs :

María Teresa González Montesinos ¹ ; Francisco Ortegón Gallego ²

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     author = {Mar{\'\i}a Teresa Gonz\'alez Montesinos and Francisco Orteg\'on Gallego},
     title = {On the existence of solutions for a strongly degenerate system},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {119--123},
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     number = {2},
     year = {2006},
     doi = {10.1016/j.crma.2006.06.002},
     language = {en},
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María Teresa González Montesinos; Francisco Ortegón Gallego. On the existence of solutions for a strongly degenerate system. Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 119-123. doi : 10.1016/j.crma.2006.06.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.06.002/

Bibliographie
Cité par

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[3] M.T. González Montesinos; F. Ortegón Gallego The evolution thermistor problem with degenerate thermal conductivity, Comm. Pure Appl. Anal., Volume 1 (2002) no. 3, pp. 313-325

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