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 ∆2–condition on the Nfunctions. 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. Mathematics Subject Classification (2010). Primary: 35K61; Secondary: 47H05.