# American Institute of Mathematical Sciences

March  2007, 6(1): 23-42. doi: 10.3934/cpaa.2007.6.23

## Existence of a capacity solution to a coupled nonlinear parabolic--elliptic system

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

Received  July 2005 Revised  September 2006 Published  December 2007

We show the existence of a capacity solution to a coupled nonlinear parabolic--elliptic system, the elliptic part in the parabolic equation being of the form -div $a(x,t,u,\nabla u)$, where the operator $a$ is of Leray--Lions type. Also, we consider the case where the elliptic equation is non-uniformly elliptic. The system may be regarded as a generalized version of the well-known thermistor problem.
Citation: Francisco Ortegón Gallego, María Teresa González Montesinos. Existence of a capacity solution to a coupled nonlinear parabolic--elliptic system. Communications on Pure & Applied Analysis, 2007, 6 (1) : 23-42. doi: 10.3934/cpaa.2007.6.23
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