Two-Scale Homogenization of Non-Linear Degenerate Evolution Equations

Using the notion of two-scale convergence developed by Allaire, the homogenization of a degenerate non-linear evolution equation with periodically oscillating coefficients is presented. A two-scale homogenized system is obtained as the limit of the periodic problem. Monotone operator methods and two-scale convergence are employed to show that the solutions of the periodic problem converge to the unique solution of the homogenized system. Homogenized initial conditions are also obtained and the sense in which they hold for the homogenized initial value problem is made specific.