Analysis for 3d degenerate cahn-larche model with periodic boundary conditions

Our aim in this article is to study the existence of weak solutions to the degenerate Cahn-Larche model. Under appropriate assumptions on the degenerate mobility and chemical free energy density, we prove the existence of weak solutions to the approximate problem with positive mobility by applying the method of continuation of local solutions, then we use the solutions of approximate problem to approach the solutions of degenerate problem. Furthermore, we perform the numerical simulations to investigate the microstructure evolution during the spinodal decomposition by utilizing this model.