Homogenization For A Class Of Nonlinear Singular Parabolic Equations

The homogenization of a class of nonlinear singular parabolic problems is studied in this dissertation.Two powerful classical methods in theory of homogenization are De Giorgi's variational convergence method and L. Tartar's energy method. For the homogenization of the partial differential equations with periodical coefficients, in 1989, Nguetseng proposed a new method, i.e., the so-called two-scale convergence method, which exploits fully the periodicity of coefficients. However, for the homogenization of degenerate or singular PDEs, there is no unified approach and we have to deal with different PDEs with different methods.Under some assumptions on the PDE and an optimal condition on Aε, L. Tartar's energy method, the classical compensated compactness arguments and monotonic methods are carefully combined to study the homogenization of the singualr parabolic problemsThe optimality of the condition (2.1.10) on Aεis also established. The result extends the conclusion of D. Cioranescu and P. Donato [1] and M.Briane [11].