Decay estimates for the classical solution of Keller–Segel system with fractional Laplacian in higher dimensions. Issue 3 (17th February 2020)

• Record Type: Journal Article
• Authors: Zhu, Shanshan; Liu, Zuhan; Zhou, Ling
• Is Part Of: Applicable analysis. Volume 99:Issue 3(2020)
• Page Start: 447
• Page End: 461
• Publication Date: 2020-02-17
• Subjects: Scott Hansen; Keller–Segel system -- fractional Laplacian -- global classical solution -- decay estimates; 35A01 -- 35B40 -- 35H10 -- 35K55; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1501030
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we investigate the generalized Keller–Segel system with two fractional parabolic equations and a classical elliptic equation in R n with n ⩾ 2 . We develop a framework for a unified treatment of the existence, uniqueness and decay estimates. With the help of selecting appropriate functional space, the existence, uniqueness and decay estimates of the global classical solution are shown at the same time under the assumption that the initial data are small enough.