Indexed by: Journal paper

First Author: Caihong Gu

Correspondence Author: Yanbin Tang

Journal: Networks and Heterogeneous Media

Included Journals: SCI

Affiliation of Author(s): Huazhong University of Science & Technology

Place of Publication: USA

Discipline: Science

First-Level Discipline: Mathematics

Document Type: J

Volume: 18

Issue: 1

Page Number: 109-139

ISSN No.: 1556-1801

Key Words: Drift-diffusion system, Keller-Segel equations, global solutions, fractional Laplacian, asymptotic behavior, multi-linear operator

DOI number: 10.3934/nhm.2023005

Date of Publication: 2023-01-01

Impact Factor: 1.41

Abstract: In this paper, we consider the global existence, regularizing decay rate and asymptotic behavior of mild solutions to Cauchy problem of fractional drift diffusion system with power-law nonlinearity. Using the properties of fractional heat semigroup and the classical estimates of fractional heat kernel, we first prove the global-in-time existence and uniqueness of the mild solutions in the frame of mixed time-space Besov space with multi-linear continuous mappings. Then, we show the asymptotic behavior and regularizing-decay rate estimates of the solution to equations with power-law nonlinearity by the method of multi-linear operator and the classical Hardy-Littlewood-Sobolev inequality.