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

In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic $p(\xb7)$-Laplacian problem with Dirichlet-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.