A blow-up dichotomy for semilinear fractional heat equations

Laister, Robert; Sierżęga, Mikolaj

Abstract

We derive a blow-up dichotomy for positive solutions of fractional semilinear heat equations on the whole space. That is, within a certain class of convex source terms, we establish a necessary and sufficient condition on the source for all positive solutions to become unbounded in finite time. Moreover, we show that this condition is equivalent to blow-up of all positive solutions of a closely-related scalar ordinary differential equation.

• Journal Article Type: Article
• Acceptance Date: Aug 14, 2020
• Online Publication Date: Sep 23, 2020
• Publication Date: 2021-10
• Deposit Date: Sep 7, 2020
• Publicly Available Date: Oct 21, 2021
• Journal: Mathematische Annalen
• Print ISSN: 0025-5831
• Electronic ISSN: 1432-1807
• Publisher: Springer (part of Springer Nature)
• Peer Reviewed: Peer Reviewed
• Volume: 381
• Pages: 75–90
• DOI: https://doi.org/10.1007/s00208-020-02078-2
• Keywords: fractional Laplacian; semilinear; heat equation; global existence; blow-up; dichotomy 2010 MSC: 35A01; 35B44; 35K58; 35R11
• Public URL: https://uwe-repository.worktribe.com/output/6664180
• Publisher URL: https://www.springer.com/gp