Blow-up for a semilinear non-local diffusion system. (December 2019)

• Record Type: Journal Article
• Authors: Ferreira, Raúl
• Is Part Of: Nonlinear analysis. Volume 189(2019)
• Publication Date: 2019-12
• Subjects: 35K57 -- 35K58 -- 35R09; Non-local diffusion -- Blow-up -- Semilinear parabolic system; 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.2019.06.023
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we study the blow-up phenomena for the system u t = ∫ Ω J ( x − y ) u ( y ) d y − u + u α v p ( x, t ) ∈ Ω × ( 0, T ) v t = ∫ Ω J ( x − y ) v ( y ) d y − v + u q v β ( x, t ) ∈ Ω × ( 0, T ) Under certain hypothesis we prove that the solution blows up infinite time and we classify in terms of the parameters when both components blow up together (simultaneous blow-up), or when only one component blows up (non-simultaneous blow-up). We also prove the blow-up rate for a particular case.