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 of mass conservation and mass dissipation. Under these assumptions, the local classical solution is shown to be global, and in the case of mass conservation or mass dissipation, to have the -norm growing at most polynomially in time. Applications include skew-symmetric Lotka-Volterra systems and quadratic reversible chemical reactions.
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Klemens Fellner, Jeff Morgan, Bao Quoc Tang, Global classical solutions to quadratic systems with mass control in arbitrary dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 2, pp. 281–307DOI 10.1016/J.ANIHPC.2019.09.003