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

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.