On the global existence and analyticity of the mild solution for the fractional Porous medium equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-14 DOI:10.1186/s13661-023-01794-3

Muhammad Zainul Abidin, Muhammad Marwan

引用次数: 0

Abstract

Abstract In this research article we focus on the study of existence of global solution for a three-dimensional fractional Porous medium equation. The main objectives of studying the fractional porous medium equation in the corresponding critical function spaces are to show the existence of unique global mild solution under the condition of small initial data. Applying Fourier transform methods gives an equivalent integral equation of the model equation. The linear and nonlinear terms are then estimated in the corresponding Lei and Lin spaces. Further, the analyticity of solution to the fractional Porous medium equation is also obtained.

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分数阶多孔介质方程温和解的整体存在性和解析性

摘要本文主要研究三维分数阶多孔介质方程整体解的存在性。在相应的临界函数空间中研究分数阶多孔介质方程的主要目的是证明在初始数据小的条件下存在唯一的全局温和解。应用傅里叶变换方法，给出了模型方程的等效积分方程。然后在相应的Lei和Lin空间中估计线性和非线性项。此外，还得到了分数阶多孔介质方程解的解析性。

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.