Capacity solution for a nonlocal thermistor problem in Solobev Spaces

Abstract

In this work, we consider a general case of the thermistor problem, in which three nonlinear terms are added to the parabolic equation governing the model. The first and second nonlinearities are present in the source term. While the third nonlinearity is considered in the evolution term. We prove the existence of a weak solution via the Schauder fixed point theorem. Consequently, we establish the existence of a capacity solution to the considered problem in Sobolev spaces.