Doubly nonlocal Fisher-KPP equation: Existence and properties of traveling waves

2018/04/26 by Dmitri Finkelshtein, Finkelshtein, Dmitri, Yuri Kondratiev +3
Mathematics · Medicine · #35C07 #35K57 #45G10 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.1804.10258

openalex publication_date 2018/04/26 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

Abstract

We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on ℝ^d. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and exponential integrability of the traveling wave profiles.

Citations

• Traveling waves and long-time behavior in a doubly nonlocal Fisher-KPP equation

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