Our aim in this article is to study generalizations of the conserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures for heat conduction and with logarithmic nonlinear terms. We obtain well-posedness results and study the asymptotic behavior of the associated system. In particular, we prove the existence of the global attractor and prove the strict separation to the pure phases in two space dimensions. Furthermore, we give some numerical simulations, obtained with the FreeFem++ software [23], comparing the conserved Caginalp phase-field type model with regular and with logarithmic nonlinear terms.

中文翻译：

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基于两个温度的麦克斯韦-卡塔尼定律的具有对数势的保守Caginalp相场系统

本文的目的是研究基于麦克斯韦-卡塔尼定律的保守Caginalp相场系统的推广，该定律具有两个导热温度和对数非线性项。我们获得了适定性结果，并研究了相关系统的渐近行为。特别是，我们证明了整体吸引子的存在，并证明了在两个空间维度上对纯相的严格分离。此外，我们给出了一些用FreeFem ++软件获得的数值模拟[23]，将守恒的Caginalp相场类型模型与正则和对数非线性项进行了比较。