A critical blow-up exponent in a chemotaxis system with nonlinear signal production. (5th April 2018)

• Record Type: Journal Article
• Authors: Winkler, Michael
• Is Part Of: Nonlinearity. Volume 31:Number 5(2018:May)
• Page Start: 2031
• Page End: 2056
• Publication Date: 2018-04-05
• Subjects: chemotaxis -- nonlinear signal production -- blow-up; 35B44 (primary) -- 35B33 -- 35K65 -- 92C17 (secondary); Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aaaa0e
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This paper is concerned with radially symmetric solutions of the Keller–Segel system with nonlinear signal production, as given by in the ball for and R > 0, where f is a suitably regular function generalizing the prototype determined by the choice, , with . The main results assert that if in this setting the number κ satisfies then for any prescribed mass level m > 0, there exist initial data u 0 with, for which the solution of the corresponding Neumann initial-boundary value problem blows up in finite time. The condition in ( ) is essentially optimal and is indicated by a complementary result according to which in the case, for widely arbitrary initial data, a global bounded classical solution can always be found.