Global classical solutions to quadratic systems with mass control in arbitrary dimensions

TL;DR

This paper proves the global existence of classical solutions for reaction-diffusion systems with quadratic nonlinearities and mass control in any dimension, including applications to ecological and chemical models.

Contribution

It establishes conditions under which solutions are globally existent and bounded, extending previous results to more general reaction-diffusion systems with mass control.

Findings

Global classical solutions exist under specified conditions.

Solutions grow at most polynomially in time with mass conservation or dissipation.

Applicable to Lotka-Volterra and reversible chemical reaction systems.

Abstract

The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass control, which includes the important cases as mass conservation and mass dissipation. Under these assumptions, the local classical solution is shown to be global and, in case of mass conservation or mass dissipation, to have $L^{\infty}$-norm growing at most polynomially in time. Applications include skew-symmetric Lotka-Volterra systems and quadratic reversible chemical reactions.