2025/02/19 by Maha Daoud, Daoud, Maha · 1 citation
Computer Science · Mathematics · #35B45 #35J62. 30G50 #35R11 #47H10 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions
paper · pdf · doi:10.48550/arxiv.2502.13771
openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove the global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems set in a bounded open subset of ℝN. The diffusion operators are of the form ui ↦ di (-Δ)Spsi ui, where 0 < si < 1. The operator (-Δ)Sps stands for the commonly called spectral fractional Laplacian. Moreover, the nonlinear reaction terms are assumed to fulfill natural structural conditions that ensure the nonnegativity of the solutions and provide uniform control of the total mass. We establish the global existence of strong solutions under the assumption that the nonlinearities exhibit at most polynomial growth. Our results extend previous results obtained when the diffusion operators are of the form ui ↦ di (-Δ)s ui, where (-Δ)s denotes the widely known regional fractional Laplacian. Furthermore, we present some numerical simulations to address a theoretical question that remains open to date.