Acceleration in integro-differential combustion equations

2021/05/20 by Émeric Bouin, Bouin, Emeric, Jérôme Coville +3
Computer Science · Mathematics · Medicine · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2105.09946

openalex publication_date 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. Our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper. To achieve this, we construct a sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty. This study involves the flattening effect occurring in accelerated propagation phenomena.

Citations

• Some theorems on stable processes
• Symmetric Stable Laws and Stable-Like Jump-Diffusions

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