Existence for a nonlocal Penrose-Fife type phase field system with inertial term

[摘要] This article presents a nonlocal Penrose-Fife type phase field system with inertial term. We do not know whether we can prove the existence of solutions to the problem as in Colli-Grasselli-Ito [3] or not. In this article we introduce a time discretization scheme, then pass to the limit as the time step h approaches 0, and obtain an error estimate for the difference between the continuous solution and the discrete solution.

[学科分类] 数学（综合）

[关键词] Nonlocal Penrose-Fife type phase field systems;inertial terms;existence;approximation and time discretization.