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Article Contents

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

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

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