Optimal conditions of non-simultaneous blow-up and uniform blow-up profiles in localized parabolic equations
Release Time:2019-03-09 Hits:
Indexed by: Journal Article
Date of Publication: 2010-01-15
Journal: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Included Journals: Scopus、EI、SCIE
Volume: 72
Issue: 2
Page Number: 867-875
ISSN: 0362-546X
Key Words: Non-simultaneous blow-up; Simultaneous blow-up; Uniform blow-up profile
Abstract: This paper deals with localized parabolic equations u(t) = Delta u + u(m)(x(0), t)e(pv(x0,t)), v(t) = Delta u + u(q)(x(0), t)e(nv(x0,f)) with homogeneous Dirichlet boundary conditions, where x(0) is any fixed point in a bounded domain of R(N). The optimal classification of non-simultaneous and simultaneous blow-up phenomena is proposed for all of the nonnegative exponents. Moreover, uniform blow-up profiles are obtained for all kinds of simultaneous blow-up solutions. (C) 2009 Elsevier Ltd. All rights reserved.