Entropy solution for a nonlinear parabolic problem with homogeneous Neumann boundary condition involving variable exponents

Abstract

In this paper we prove the existence and uniqueness of an entropy solution for a non-linear parabolic equation with homogeneous Neumann boundary condition and initial data in $L^{1}.$ By a time discretization technique we analyze the existence, uniqueness and stability questions. The functional setting involves Lebesgue and Sobolev spaces with variable exponents.

Keywords

• nonlinear parabolic problem
• variable exponents
• entropy solution
• neumann-type boundary conditions
• semi-discretization