涉及Laplace-Beltrami算子的偏微分方程系统的存在性、唯一性和集中性

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries Pub Date : 2019-05-09 DOI:10.4171/IFB/416

M. Amar, R. Gianni

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引用次数: 4

摘要

在本文中，我们推导了一个复合介质中的热扩散模型，其中不同组分被热活性界面分离。先前的结果是通过集中容量过程得到的，并导致了涉及作用于界面上的拉普拉斯-贝尔特拉米算子的非稳态偏微分方程系统。利用压缩映射和抽象抛物问题理论证明了该系统的适定性。最后，证明了系统解在时间上的指数收敛性。2010年数学学科分类:小学35K20;二级35K90, 35B40。

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Existence, uniqueness and concentration for a system of PDEs involving the Laplace–Beltrami operator

In this paper we derive a model for heat diffusion in a composi te medium in which the different components are separated by thermally active interf ac s. The previous result is obtained via a concentrated capacity procedure and leads to a non-sta ntard system of PDEs involving a Laplace-Beltrami operator acting on the interface. For suc h a system well-posedness is proved using contraction mapping and abstract parabolic problems theory. Finally, the exponential convergence (in time) of the solutions of our system to a steady s tate is proved. 2010 Mathematics Subject Classification: Primary 35K20; Secondary 35K90, 35B40.

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来源期刊

Interfaces and Free Boundaries 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Interfaces and Free Boundaries is dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems in all areas where such phenomena are pertinent. The journal aims to be a forum where mathematical analysis, partial differential equations, modelling, scientific computing and the various applications which involve mathematical modelling meet. Submissions should, ideally, emphasize the combination of theory and application.