Existence for a singular nonlocal phase field system with inertial term

Shunsuke Kurima

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arXiv · 2105.07461

Existence for a singular nonlocal phase field system with inertial term

Shunsuke Kurima

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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 $\theta$ under time derivative. Although the system has a difficult mathematical point caused by the combination of $(\ln \theta)_{t}$, the inertial term and the nonlocal diffusion term for the order parameter $\varphi$ (see Section 1.1), we can establish existence of solutions by a key estimate (see Remark 1.1).

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Shunsuke Kurima. 2021-05-16. Existence for a singular nonlocal phase field system with inertial term. https://arxiv.org/abs/2105.07461

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