On the global existence and uniform-in-time bounds for three-component reaction-diffusion systems with mass control and polynomial growth

2025/10/31 by Redouane Douaifia, Douaifia, Redouane, Salem Abdelmalek +3
Engineering · Mathematics · Medicine · #Stability and Controllability of Differential Equations #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models

paper · pdf · doi:10.48550/arxiv.2510.27555

Abstract

We investigate a class of three-component reaction-diffusion systems subject to mass control and a newly introduced structural assumption, referred to as linear intermediate weighted sum condition. Under these hypotheses, we establish the global existence of classical solutions in arbitrary spatial dimensions and wide class of boundary conditions, even when the nonlinearities exhibit arbitrary polynomial growth. We establish also that, under slight-stronger assumptions and mixed boundary conditions, solutions admit uniform-in-time bounds. Our approach relies on the extension of L^p-energy polynomial functionals, together with the regularizing effect for parabolic equations. Furthermore, we demonstrate the applicability of our framework by analyzing three-species sub-skew-symmetric Lotka-Volterra systems with higher-order interactions.

Citations

• Uniform-in-time bounds for quadratic reaction-diffusion systems with\n mass dissipation in higher dimensions
• Solutions of the 4-species quadratic reaction-diffusion system are\n bounded and C^\∞, in any space dimension
• On the entropic structure of reaction-cross diffusion systems
• Entropy, Duality and Cross Diffusion
• Inhomogeneous Parabolic Neumann Problems
• Global regularity of solutions to systems of reaction-diffusion with Sub-Quadratic Growth in any dimension

Related

• Analysis of mass controlled reaction-diffusion systems with nonlinearities having critical growth rates
• Global classical solutions to quadratic systems with mass control in arbitrary dimensions
• Uniform-in-time bounds for quadratic reaction-diffusion systems with\n mass dissipation in higher dimensions
• Global classical solutions for mass-conserving, (super)-quadratic reaction-diffusion systems in three and higher space dimensions
• Volume-surface systems with sub-quadratic intermediate sum on the surface: Global existence and boundedness