Uniform-in-time bounds for quadratic reaction-diffusion systems with mass dissipation in higher dimensions

Klemens Fellner, ,Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria, Jeff Morgan, Bao Quoc Tang, ,Department of Mathematics, University of Houston, Houston, Texas 77004, USA, ,Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010 Graz, Austria
2018 Discrete and Continuous Dynamical Systems. Series S  
Uniform-in-time bounds of nonnegative classical solutions to reactiondiffusion systems in all space dimension are proved. The systems are assumed to dissipate the total mass and to have locally Lipschitz nonlinearities of at most (slightly super-) quadratic growth. This pushes forward the recent advances concerning global existence of reaction-diffusion systems dissipating mass in which a uniform-in-time bound has been known only in space dimension one or two. As an application, skew-symmetric
more » ... on, skew-symmetric Lotka-Volterra systems are shown to have unique classical solutions which are uniformly bounded in time in all dimensions with relatively compact trajectories in C(Ω) m . 2010 Mathematics Subject Classification. 35A01, 35K57, 35K58, 35Q92, 92D25.
doi:10.3934/dcdss.2020334 fatcat:rbkrko7pxzhvtp7uyf33bcaska