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

Francisco Ortegón Gallego; María Teresa González Montesinos

doi:10.3934/cpaa.2007.6.23

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2007, Volume 6, Issue 1: 23-42. Doi: 10.3934/cpaa.2007.6.23

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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
2.
Departmento de Matemáticas, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, 11002 Cádiz

Received: June 30, 2005

Revised: August 31, 2006

Published: February 2007

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Abstract

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.

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Mathematics Subject Classification: Primary: 35M10, 35J60, 35K65; Secondary: 35J70.

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