卡吉纳普相场型方程解的稳定性

M. Ipopa, Brice Landry Doumbé Bangola, Armel Andami Ovono
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引用次数: 0

摘要

本文研究的是卡吉纳普相场模型广义化的渐近行为,该模型受均质诺伊曼边界条件和涉及两个温度的正则势的约束。该论文证明了问题的拟合性、系统的耗散性以及全局吸引子和指数吸引子的存在。此外,还对半无限圆柱体进行了研究。事实上,如果说全局吸引子的存在确实可以预测有界域上解的渐近行为,但这并不意味着这些解会收敛。因此,在证明了全局吸引子的存在之后,必须研究解随时间的收敛性。有几种方法可以确定微分系统解的渐近行为。其中之一是将给定的微分方程转化为积分方程,然后对其应用经典的皮卡尔连续逼近程序。这项工作致力于研究解向稳定状态的收敛性,采用了关于 Lojasiewicz-Simon 不等式的著名结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stability of Solutions to a Caginalp Phase-Field Type Equations
This paper is concerned with the study of the asymptotic behavior of a generalization of the Caginalp phase-field model subject to homogeneous Neumann boundary conditions and regular potentials involving two temperatures. This work follows on from a paper in which the well-posedness of the problem, the dissipativity of the system, and the existence of global and exponential attractors were demonstrated. In addition, a study on the semi-infinite cylinder was also carried out. Indeed, if it is true that the existence of a global attractor makes it possible to predict the asymptotic behavior of solutions on a bounded domain, it does not say that these solutions converge. After having shown the existence of the global attractor, it is therefore important to look at the convergence of the solutions over time. There are several methods for determining the asymptotic behavior of the solutions of a differential system. We can mention the one that consists of transforming the given differential equations into integral equations and then applying the classical Picard successive approximation procedure to them. This work is devoted to the study of the convergence of solutions to steady states, adapting a well-known result concerning Lojasiewicz-Simon’s inequality.
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