Homogenization of a nonlinear degenerate parabolic differential equation

Abstract

This paper is devoted to the homogenization of a nonlinear degenerate parabolic problem $$\partial _t u^\varepsilon - div\left( {D\left( {\frac{x} {\varepsilon },u^\varepsilon ,\nabla u^\varepsilon } \right) + K\left( {\frac{x} {\varepsilon },u^\varepsilon } \right)} \right) = f(x)$$ with Dirichlet boundary condition. Here the operator D(y, s,∇s) is periodic in y and degenerated in ∇s. In the paper, under the two-scale convergence theory, we obtain the limit equation as e → 0 and also prove the corrector results of ▽ue to strong convergence.