Existence of entropy solutions to nonlinear degenerate parabolic problems with variable exponent and L1-data

In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic p(·)-Laplacian problem with Dirichlet-type boundary conditions and L1 data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.