各向异性Hölder空间中分数阶各向异性抛物方程的Cauchy问题

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-23 DOI:10.3934/eect.2022029

S. Degtyarev

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引用次数: 0

摘要

考虑各向异性Hölder空间中分数阶各向异性抛物方程的Cauchy问题。这个方程将热方程推广到拉普拉斯算子的分数次幂的情况这个算子的幂对于不同的空间变量组是不同的。时间导数可以是分数阶的Caputo - jbashyan导数，也可以是通常的导数。在时间导数阶的必要条件下，我们证明了整个问题的算子是适当各向异性Hölder空间的同构。在另一些条件下，我们证明了柯西问题在相同空间中的唯一可解性。

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Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces

We consider a Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces. The equation generalizes the heat equation to the case of fractional power of the Laplace operator and the power of this operator can be different with respect to different groups of space variables. The time derivative can be either fractional Caputo - Jrbashyan derivative or usual derivative. Under some necessary conditions on the order of the time derivative we show that the operator of the whole problem is an isomorphism of appropriate anisotropic Hölder spaces. Under some another conditions we prove unique solvability of the Cauchy problem in the same spaces.

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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.