Qualitative properties of fractional convolution elliptic and parabolic operators in Besov spaces

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-06-21 DOI:10.1007/s13540-024-00302-3

Veli Shakhmurov, Rishad Shahmurov

引用次数: 0

Abstract

The maximal \(B_{p,q}^{s}\)-regularity properties of a fractional convolution elliptic equation is studied. Particularly, it is proven that the operator generated by this nonlocal elliptic equation is sectorial in \( B_{p,q}^{s}\) and also is a generator of an analytic semigroup. Moreover, well-posedeness of nonlocal fractional parabolic equation in Besov spaces is obtained. Then by using the \(B_{p,q}^{s}\)-regularity properties of linear problem, the existence, uniqueness of maximal regular solution of corresponding fractional nonlinear equation is established.

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贝索夫空间中分数卷积椭圆和抛物线算子的定性特性

研究了分数卷积椭圆方程的最大 \(B_{p,q}^{s}\-regularity 特性。特别是，研究证明了由该非局部椭圆方程产生的算子在 \( B_{p,q}^{s}\) 中是扇形的，同时也是一个解析半群的生成器。此外，我们还得到了非局部分数抛物方程在 Besov 空间中的好拟性。然后利用线性问题的 \(B_{p,q}^{s}\)-正则性质，建立了相应分数非线性方程最大正则解的存在性和唯一性。

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

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.