Nonlocal nonlinear reaction preventing blow-up in supercritical case of chemotaxis system. (November 2018)

• Record Type: Journal Article
• Authors: Bian, Shen; Chen, Li; Latos, Evangelos A.
• Is Part Of: Nonlinear analysis. Volume 176(2018)
• Page Start: 178
• Page End: 191
• Publication Date: 2018-11
• Subjects: Chemotaxis model -- Fisher–KPP model -- Global existence -- Nonlocal reaction; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2018.06.012
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is devoted to the analysis of non-negative solutions for the chemotaxis model with nonlocal nonlinear source in bounded domain. The qualitative behavior of solutions is determined by the nonlinearity from the aggregation and the reaction. When the growth factor is stronger than the dampening effect, with the help of the nonlocal nonlinear term in the reaction, for appropriately chosen exponents and arbitrary initial data, the model admits a classical solution which is uniformly bounded. Moreover, when the growth factor has the same order with the dampening effect, the nonlocal nonlinear exponents can prevent the chemotactic collapse.