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

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