Blow-up analysis for a reaction–diffusion equation with weighted nonlocal inner absorptions under nonlinear boundary flux. (December 2016)

• Record Type: Journal Article
• Authors: Ma, Lingwei; Fang, Zhong Bo
• Is Part Of: Nonlinear analysis. Volume 32(2016)
• Page Start: 338
• Page End: 354
• Publication Date: 2016-12
• Subjects: Reaction–diffusion equation -- Weighted nonlocal absorption -- Global existence -- Blow-up time -- Upper bound -- Lower bound; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.05.005
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: A blow-up analysis for a nonlinear divergence form reaction–diffusion equation with weighted nonlocal inner absorption terms is considered under nonlinear boundary flux in a bounded star-shaped region. Based on the auxiliary function method and the modified differential inequality technique, we establish conditions on weight function and nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, upper and lower bounds for the blow-up time are derived under appropriate measure in higher dimensional spaces. Three examples are presented to illustrate applications of our main results.