Comptes Rendus
Partial Differential Equations
On the existence of solutions for a strongly degenerate system
[Sur l'existence de solutions pour un système fortement dégénéré]
Comptes Rendus. Mathématique, Volume 343 (2006) no. 2, pp. 119-123.

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 diva(x,t,u,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 diva(x,t,u,u), where a is an operator of the Leray–Lions type. Moreover, the second equation is nonuniformly elliptic.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.06.002

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
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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/

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