Homogenization of a nonlinear degenerate parabolic differential equation

Abstract

In this article, we study the homogenization of the nonlinear degenerate parabolic equation $$ partial_t b({x /varepsilon},u_varepsilon) - mathop{ m div} a({x /varepsilon},{t /varepsilon}, u_varepsilon,abla u_varepsilon)=f(x,t), $$ with mixed boundary conditions(Neumann and Dirichlet) and obtain the limit equation as $varepsilon o 0$. We also prove corrector results to improve the weak convergence of $abla u_varepsilon$ to strong convergence.

Keywords

• degenerate parabolic equation
• homogenization
• two-scale convergence
• correctors.