A doubly nonlinear evolution problem related to a model for microwave heating

Abstract

This paper is concerned with the existence and uniqueness of the solution to a doubly nonlinear parabolic problem which arises directly from a circuit model of microwave heating. Beyond the relevance from a physical point of view, the problem is very interesting also in a mathematical approach: in fact, it consists of a nonlinear partial differential equation with a further nonlinearity in the boundary condition. Actually, we are going to prove a general result: the two nonlinearities are allowed to be maximal monotone operators and then an existence result will be shown for the resulting problem.