2023/12/15 by Émeric Bouin, Bouin, Emeric, Jérôme Coville +3
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2312.09614
openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper focuses on propagation phenomena in reaction-diffusion equations with a weaklymonostable nonlinearity. The reaction term can be seen as an intermediate between the classicallogistic one (or Fisher-KPP) and the standard weak Allee effect one. We investigate the effect ofthe decay rate of the initial data on the propagation rate. When the right tail of the initial datais sub-exponential, finite speed propagation and acceleration may happen and we derive the exactseparation between the two situations. When the initial data is sub-exponentially unbounded, accel-eration unconditionally occurs. Estimates for the locations of the level sets are expressed in termsof the decay of the initial data. In addition, sharp exponents of acceleration for initial data withsub-exponential and algebraic tails are given. Numerical simulations are presented to illustrate theabove findings.