Blow-up of positive solutions to a singular Gierer–Meinhardt system. (August 2019)

• Record Type: Journal Article
• Authors: Chen, Shaohua; Xu, Runzhang
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 326
• Page End: 336
• Publication Date: 2019-08
• Subjects: Blow up of solutions -- Singular Gierer–Meinhardt systems -- Dirichlet boundary conditions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.010
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper deals with blow-up of positive solutions for a singular Gierer–Meinhardt system subject to zero Dirichlet boundary conditions. We first prove the existence of a local solution and then show blow-up solutions under certain conditions for parameters. We use a functional method to obtain a local solution which is bounded by the first eigenfunction both from above and from below and then obtain the bound of a ratio of two solutions. This method is completely different from the traditional methods of sub and super solutions.