A NEW CLASS OF DOUBLY NONLINEAR EVOLUTION EQUATIONS

Abstract

In this paper we consider the solvability for a new class of doubly nonlinear evolution equations. The motivation of this work comes from a transmission problem of two degenerate parabolic equations with convection term, in which the transmission boundary is time-dependent. We give an abstract existence result, and show that the weak variational formulation for the transmission problem can be solved by applying this abstract result. In our existence proof, the abstract theory of pseudo-monotone operators is useful.