Blow-up and global solutions for a class of time fractional nonlinear reaction–diffusion equation with weakly spatial source. (May 2019)

• Record Type: Journal Article
• Authors: Cao, Jianxiong; Song, Guojie; Wang, Jie; Shi, Qihong; Sun, Sujing
• Is Part Of: Applied mathematics letters. Volume 91(2019)
• Page Start: 201
• Page End: 206
• Publication Date: 2019-05
• Subjects: Fractional nonlinear reaction–diffusion equation -- Blow-up -- Global solution; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2018.12.020
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: This paper investigates the blow-up of solutions for a time fractional nonlinear reaction–diffusion equation with weakly spatial source. We first derive two sufficient conditions under which the solutions may blow up in finite time. Then, we prove the existence of global solution when the initial data are small enough. Moreover, the long time behavior of bounded solutions will be analyzed.