Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 40, pp. 1-18.

Title: Existence for a nonlocal Penrose-Fife type phase field system with inertial term
       
Author: Shunsuke Kurima (Tokyo Univ. of Science, Japan)

Abstract:
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.

Submitted March 29, 2022. Published June 23, 2023.
Math Subject Classifications: 35G30, 80A22, 35A40.
Key Words: Nonlocal Penrose-Fife type phase field systems; inertial terms; existence; approximation and time discretization