Global Solutions in the 2‐D Case of a Degenerate Phase‐Field Model for Spinodal Decomposition

ABSTRACT We study an initial‐boundary value problem for a novel phase‐field model describing the evolution of spinodal decomposition, a typical example of solid‐phase separation. The nonuniform, degenerate parabolic evolution equation in the model differs from the classical Cahn–Hilliard equation by a nonsmooth gradient term of the order parameter. The existing results are mostly limited to one‐dimensional cases, and this paper aims to extend the results to two‐dimensional spaces. We prove the global existence of weak solutions to this model and use the model to simulate the microstructural evolution of phase separation.