A mathematical analysis of a nonisothermal Allen-Cahn type system

摘要

Existence of solutions for a nonisothermal Allen-Cahn type system is proved by using a semidiscrete spectral Galerkin method together with degree theory and maximum principle. Regularity and uniqueness are obtained in a special situation for domains with dimension up to two and smooth enough data. The present system may model the evolution of solidification or melting processes occurring in certain binary alloys.