Asymptotic behaviour of a phase field system derived from a generalization of Maxwell–Cattaneo’s law with a singular potential

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Brice Landry Doumbé Bangola, Mohamed Ali Ipopa, Armel Andami Ovono
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引用次数: 0

Abstract

In this paper, we study the asymptotic behaviour of a Caginalp-type phase field system derived from a heat conduction law which is a generalization of the Maxwell–Cattanéo law and whose potential is singular. This type of law has the advantage of correcting the paradox of heat conduction that appears when the Fourier law is considered. The potential considered is typically logarithmic. Using such a potential makes the model much more relevant from a physical point of view. However, from a theoretical point of view, it is essential to obtain the strict separation property of the phase field in order to give sense of the equations. We first prove the existence and uniqueness of the solution thanks to the separation property. We also address the question of the dissipativity of the system. Finally, we obtain the existence of the global attractor.
由具有奇异势能的麦克斯韦-卡塔尼奥定律广义推导出的相场系统的渐近行为
在本文中,我们研究了一个卡吉纳普型相场系统的渐近行为,该系统由热传导定律衍生而来,而热传导定律是麦克斯韦-卡塔内奥定律的一般化,其势能是奇异的。这种定律的优点是纠正了在考虑傅立叶定律时出现的热传导悖论。所考虑的电势通常是对数。从物理角度来看,使用这种势能使模型更加贴切。然而,从理论角度来看,必须获得相场的严格分离特性,才能使方程具有意义。我们首先利用分离特性证明了解的存在性和唯一性。我们还讨论了系统的耗散性问题。最后,我们得到了全局吸引子的存在性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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