Existence of a capacity solution to a nonlinear parabolic–elliptic coupled system in anisotropic Orlicz-Sobolev spaces

Abstract

In this work, we show the existence of a capacity solution for a nonlinear coupled parabolic–elliptic system in inhomogeneous anisotropic Orlicz-Sobolev spaces without assuming the Δ2-condition on the N-functions. This system describes the heat surge generated within a semiconductor device by an electrical direct current. This may be seen as a generalization of the so-called thermistor problem.

Keywords

• Nonlinear parabolic equations
• Monotone operators
• Weak solution
• Capacity solution
• Inhomogeneous anisotropic Orlicz-Sobolev spaces
• Thermistor problem