A sufficient condition of sensitivity functions for boundedness of solutions to a parabolic-parabolic chemotaxis system. (12th March 2018)

• Record Type: Journal Article
• Authors: Fujie, Kentarou; Senba, Takasi
• Is Part Of: Nonlinearity. Volume 31:Number 4(2018:Apr.)
• Page Start: 1639
• Page End: 1672
• Publication Date: 2018-03-12
• Subjects: chemotaxis -- sensitivity function -- time-global existence; 35B45 -- 35K45 -- 35Q92 -- 92C17; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaa2df
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This paper deals with time-global solutions to the parabolic system under the homogeneous Neumann boundary conditions in a bounded and convex domain ( ) with smooth boundary . Here τ is a positive parameter, χ is a smooth function on satisfying and is a pair of nonnegative initial data. We will consider the above system as a perturbation of a nonlocal parabolic equation and establish a sufficient condition of the sensitivity function χ for the global existence of solutions under the assumption of smallness of the constant τ .