Large time behavior of a two phase extension of the porous medium equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-03-28 DOI:10.4171/IFB/421

A. Oulhaj, C. Cancès, C. Chainais-Hillairet, Philippe Laurencçot

引用次数: 7

Abstract

We study the large time behavior of the solutions to a two phase extension of the porous medium equation, which models the so-called seawater intrusion problem. The goal is to identify the self-similar solutions that correspond to steady states of a rescaled version of the problem. We fully characterize the unique steady states that are identified as minimizers of a convex energy and shown to be radially symmetric. Moreover, we prove the convergence of the solution to the time-dependent model towards the unique stationary state as time goes to infinity. We finally provide numerical illustrations of the stationary states and we exhibit numerical convergence rates.

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多孔介质方程两相扩展的大时间行为

我们研究了模拟海水入侵问题的多孔介质方程的两相扩展解的大时间行为。目标是识别与问题的缩放版本的稳定状态相对应的自相似解决方案。我们完全描述了唯一的稳定状态，被确定为一个凸能量的最小值，并显示为径向对称。此外，我们还证明了当时间趋于无穷时，时间依赖模型解向唯一定态的收敛性。我们最后提供了稳态的数值说明，并展示了数值收敛速率。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.