A mathematical analysis of a nonisothermal Allen-Cahn type system: Error estimates

摘要

In this article, under certain conditions, we prove the regularity for the solutions of an Allen-Cahn phase-field type system obtained as limits of approximate solutions constructed by using a semidiscrete spectral Galerkin method. With the help of this improved regularity, as one compares to previous results, we then derive error estimates for the approximate solutions in terms of the inverse of the eigenvalues of the Laplacian operator. The system under investigation may model the evolution of solidification or melting of certain binary alloys.