奇异热方程解的长时间行为及其在流体力学中的应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2018-10-04 DOI:10.4171/ifb/437

G. Kitavtsev, R. Taranets

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引用次数: 1

摘要

本文推广了[1]的结果，证明了在拉格朗日坐标系下具有L^2源项的一维奇异热方程解的指数渐近H^1收敛性。进一步，我们将这一渐近收敛结果推广到时间非齐次源的情况。本研究对多孔介质方程理论也有独立的兴趣。

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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Long-time behaviour of solutions to a singular heat equation with an application to hydrodynamics

In this paper, we extend the results of [1] by proving exponential asymptotic $H^1$-convergence of solutions to a one-dimensional singular heat equation with $L^2$-source term that describe evolution of viscous thin liquid sheets while considered in the Lagrange coordinates. Furthermore, we extend this asymptotic convergence result to the case of a time inhomogeneous source. This study has also independent interest for the porous medium equation theory.

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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.

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