Global existence and blowup solutions for the Gierer–Meinhardt system. (July 2020)

• Record Type: Journal Article
• Authors: Chen, Shaohua; Melnick, Brittney; Xu, Runzhang
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: Global existence -- Blowup solutions -- Gierer–Meinhardt systems; 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.2020.111785
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We discuss global and blowup solutions for general Gierer–Meinhardt system with zero Neumann boundary conditions, which originally arose in studies of pattern-formation in biology and has interesting and challenging mathematical properties. We obtain some new sufficient conditions for global existence and finite time blow-up of solutions. In some special cases, the results are sharp.