On the stability of the state 1 in the non-local Fisher-KPP equation in\n bounded domains

2018/01/17 by Camille Pouchol, Pouchol, Camille
Computer Science · Mathematics · Medicine · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1801.05653

openalex publication_date 2018/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the non-local Fisher-KPP equation on a bounded domain with\nNeu-mann boundary conditions. Thanks to a Lyapunov function, we prove that\nunder a general hypothesis on the Kernel involved in the non-local term, the\nhomogenous steady state 1 is globally asymptotically stable. This assumption\nhappens to be linked to some conditions given in the literature, which ensure\nthat travelling waves link 0 to 1.\n

Citations

• Convergence to equilibrium for positive solutions of some mutation-selection model
• Global Stability in Many-Species Systems

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