Rothe time-discretization method for a nonlinear parabolic p(u) -Laplacian problem with Fourier-type boundary condition and $$L^1$$-data

Abstract

In this paper, we prove the existence and uniqueness results of entropy solutions to a class of nonlinear parabolic p(u)-Laplacian problem with Fourier-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.