Blow-up analyses in reaction–diffusion equations with Fujita exponents. (December 2019)

• Record Type: Journal Article
• Authors: Li, Fengjie; Lin, Hongyan; Liu, Bingchen
• Is Part Of: Nonlinear analysis. Volume 50(2019)
• Page Start: 386
• Page End: 412
• Publication Date: 2019-12
• Subjects: Fujita exponent -- Blow-up rate -- Blow-up set -- Blow-up time; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.05.009
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, we study the reaction–diffusion equations with variable coefficients in some bounded domains. At least one of the components of solutions blows up for every initial data in some exponent regions, where the Fujita exponents are determined by the exponents of the sources and the coefficients and the dimension of the domain. We also show the classifications of simultaneous and nonsimultaneous blow-up of the components of solutions. The asymptotic properties are discussed including blow-up rates and sets. Moreover, the upper and the lower bounds of blow-up time are given for all dimensions of domains, respectively.