奇异热方程解的长时间行为及其在流体力学中的应用

IF 1.2 4区数学 Q1 MATHEMATICS

Interfaces and Free Boundaries 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

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.