Blowup of a free boundary problem with a nonlocal reaction term. (June 2018)

• Record Type: Journal Article
• Authors: Yang, Jian
• Is Part Of: Nonlinear analysis. Volume 41(2018)
• Page Start: 529
• Page End: 537
• Publication Date: 2018-06
• Subjects: Nonlinear reaction–diffusion equation -- One-phase Stefan problem -- Decay -- Blowup; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.11.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a blowup problem of a reaction–diffusion equation with a nonlocal reaction term. Such a problem arises in the description of the species inhabiting in a region surrounded by an inhospitable area with the free boundary representing the spreading front of the species. Firstly, we give some sufficient conditions for finite time blowup. Then we show that the solution decays at an exponential rate and the two free boundaries converge to a finite limit provided the initial data is small and the result is different for the positive and non-positive growth rate.