Properties of non-simultaneous blow-up solutions in nonlocal parabolic equations

• Published in: Nonlinear analysis Vol. 72; no. 2; pp. 1065 - 1074
• Main Authors: Liu, Bingchen, Li, Fengjie
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.01.2010; Elsevier
• Subjects: Blow-up rate; Criteria; Dirichlet problem; Exact sciences and technology; Mathematical analysis; Mathematics; Non-simultaneous blow-up; Nonlinearity; Partial differential equations; Sciences and techniques of general use; Simultaneous blow-up; Single point blow-up; Total blow-up; Simultaneous blow-up; Single point blow-up; Non-simultaneous blow-up; Total blow-up; Blow-up rate; Primary; Parabolic equation; 35K60; Nonlinear analysis; 35B33; Primary 35K05; 35B40; Mathematical model
• ISSN: 0362-546X; 1873-5215
• DOI: 10.1016/j.na.2009.07.046

This paper deals with blow-up solutions in parabolic equations coupled via nonlocal nonlinearities, subject to homogeneous Dirichlet conditions. Firstly, some criteria on non-simultaneous and simultaneous blow-up are given, including four kinds of phenomena: (i) the existence of non-simultaneous blow-up; (ii) the coexistence of non-simultaneous and simultaneous blow-up; (iii) any blow-up must be simultaneous; (iv) any blow-up must be non-simultaneous. Next, total versus single point blow-up are classified completely. Moreover, blow-up rates are obtained for both non-simultaneous and simultaneous blow-up solutions.