2025/01/05 by Phuoc‐Tai Nguyen, Nguyen, Phuoc-Tai, Bao Quoc Tang +1
Computer Science · Engineering · Mathematics · #35A01 #35K57 #35K58 #35Q92 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2501.02603
openalex publication_date 2025/01/05 · openalex created_date 2025/01/08 · openalex updated_date 2026/07/28
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space \mathbb RN is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate total mass. We first show that if the nonlinearities are at most quadratic then there exists a unique global bounded solution regardless of the fractional order. This is done by combining a regularizing effect of the fractional diffusion operator and the Hölder continuity of a non-local inhomogeneous parabolic equation. When the nonlinearities might be super-quadratic, but satisfy some intermediate sum conditions, we prove the global existence of bounded solutions by adapting the well-known duality methods to the case of fractional diffusion. In this case, the order of the intermediate sum conditions depends on the fractional order. These results extend the existing theory for mass dissipated reaction-diffusion systems to the case of non-local diffusion and unbounded domains.