Global existence of solutions to a two dimensional attraction–repulsion chemotaxis system in the attractive dominant case with critical mass. (January 2020)

• Record Type: Journal Article
• Authors: Nagai, Toshitaka; Yamada, Tetsuya
• Is Part Of: Nonlinear analysis. Volume 190(2020)
• Publication Date: 2020-01
• Subjects: 35B45 -- 35K15 -- 35K55; Attraction–repulsion chemotaxis system -- a priori estimate -- Global existence; 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.2019.111615
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We study the Cauchy problem for an attraction–repulsion chemotaxis system in two dimensions: ∂ t u = Δ u − ∇ ⋅ ( u ∇ ( β 1 v 1 − β 2 v 2 ) ), 0 = Δ v 1 − λ 1 v 1 + u, 0 = Δ v 2 − λ 2 v 2 + u with nonnegative initial data u 0 and positive constants β 1, β 2, λ 1, λ 2 . The purpose of this paper is to show that the Cauchy problem admits the global nonnegative solutions in time if ( β 1 − β 2 ) ∫ R 2 u 0 d x = 8 π in the attractive dominant case β 1 > β 2 .