Existence and stability of curved fronts for spatially periodic combustion reaction-diffusion equations in ℝ^N

2025/10/24 by Wei-Jie Sheng, Sheng, Wei-Jie, Xintian Zhang +1
Computer Science · Mathematics · Medicine · #35B10 #35K10 #35K15 #35K57 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2510.21163

openalex publication_date 2025/10/24 · openalex created_date 2025/10/28 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with curved fronts of combustion reaction-diffusion equations in spatially periodic media in ℝ^N (N≥2). Under the assumption that there are moving pulsating fronts for any given propagation direction e ∈ \mathbbS^N-1, and by constructing suitable super- and sub-solutions, we prove the existence of a curved front with polytope-like shape in ℝ^N. Then we show that the curved front is unique and asymptotically stable.

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