2019/06/17 by Klemens Fellner, Fellner, Klemens, Jeffrey R. Morgan +3 · 2 citations
Mathematics · Medicine · #35A01 #35K57 #35K58 #35Q92 #92D25 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1906.06902
openalex publication_date 2019/06/17 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Uniform-in-time bounds of nonnegative classical solutions to\nreaction-diffusion systems in all space dimension are proved. The systems are\nassumed to dissipate the total mass and to have locally Lipschitz\nnonlinearities of at most (slightly super-) quadratic growth. This pushes\nforward the recent advances concerning global existence of reaction-diffusion\nsystems dissipating mass in which a uniform-in-time bound has been known only\nin space dimension one or two. As an application, skew-symmetric Lotka-Volterra\nsystems are shown to have unique classical solutions which are uniformly\nbounded in time in all dimensions with relatively compact trajectories in\nC(\\Ω)m.\n