The threshold phenomena for propagation in fractional Laplacian diffusion equations

Discrete and Continuous Dynamical Systems - S 2026 Open access

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Authors: Grégory Faye, Min Zhao
DOI: 10.3934/dcdss.2026099
Cited by: 1
References: 29

Abstract

In this paper, we investigate the threshold phenomenon between extinction and propagation in fractional Laplacian diffusion equations for a class of compactly supported initial data. We provide the first quantitative estimates on the threshold when the reaction nonlinearity is of bistable or ignition type. We mainly use estimates on the fundamental solutions of fractional Laplacian operators together with some accurate upper and lower solutions to show that the solution either propagates or goes extinct.

Fields of Study & Subjects

Fractional Differential Equations Solutions Mathematical and Theoretical Epidemiology and Ecology Models Differential Equations and Numerical Methods

Publication details

Journal / source
Discrete and Continuous Dynamical Systems - S
Publisher
American Institute of Mathematical Sciences (AIMS)
Volume
31
Issue
0
Pages
407–430
Publication date
20 March 2026
Language
EN