Anisotropic and isotropic persistent singularities of solutions of the fast diffusion equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-11-15 DOI:10.57262/die035-1112-729

M. Fila, Petra Mackov'a, J. Takahashi, E. Yanagida

引用次数: 4

Abstract

Abstract. The aim of this paper is to study a class of positive solutions of the fast diffusion equation with specific persistent singular behavior. First, we construct new types of solutions with anisotropic singularities. Depending on parameters, either these solutions solve the original equation in the distributional sense, or they are not locally integrable in space-time. We show that the latter also holds for solutions with snaking singularities, whose existence has been proved recently by M. Fila, J.R. King, J. Takahashi, and E. Yanagida. Moreover, we establish that in the distributional sense, isotropic solutions whose existence was proved by M. Fila, J. Takahashi, and E. Yanagida in 2019, actually solve the corresponding problem with a moving Dirac source term. Last, we discuss the existence of solutions with anisotropic singularities in a critical case.

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快速扩散方程解的各向异性和各向同性持久奇点

摘要研究一类具有特定持久奇异行为的快速扩散方程的正解。首先，构造了具有各向异性奇异点的新型解。根据参数的不同，这些解要么在分布意义上解原方程，要么在时空中不局部可积。我们证明后者也适用于具有蛇形奇点的解，蛇形奇点的存在性最近已被M. Fila, J.R. King, J. Takahashi和E. Yanagida证明。此外，我们建立了在分布意义上，M. Fila, J. Takahashi和E. Yanagida在2019年证明的各向同性解的存在性实际上解决了带有移动Dirac源项的相应问题。最后，讨论了一类临界情况下各向异性奇异解的存在性。

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.