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

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.