Existence for a singular nonlocal phase field system with inertial term

2021/05/16 by Kurima, Shunsuke
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.07461

Abstract

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 (ln θ)_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).

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