Doubly nonlinear parabolic equations with variable exponents of nonlinearity

Abstract

We investigate a mixed problem for a class of parabolic-type equations with double nonlinearity and minor terms that do not degenerate and whose indexes of nonlinearity are functions of spatial variables. These problems are considered in the generalized Lebesgue and Sobolev spaces. We obtain conditions for the existence of the generalized solution of this problem by using the Galerkin method.