Existence of entropy solutions to nonlinear parabolic problems with variable exponent and $$L^1$$ L 1 -data

Abstract

In the present paper we prove existence results of entropy solutions to a class of nonlinear parabolic p(.)-Laplacian problem with Neumann-type boundary conditions and \(L^1\) data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.