In this paper we deal with a singular nonlocal phase field system with inertial term. The system has the logarithm of the absolute temperature θ under time derivative. Although the system has a difficult mathematical point caused by the combination of (lnθ)t, the inertial term and the nonlocal diffusion term for the order parameter φ (see Section 1.1), we can establish existence of solutions by a key estimate (see Remark 1.1).
@article{arxiv.2105.07461,
title = {Existence for a singular nonlocal phase field system with inertial term},
author = {Shunsuke Kurima},
journal= {arXiv preprint arXiv:2105.07461},
year = {2021}
}