Uniform-in-time bounds of nonnegative classical solutions to reaction-diffusion 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 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(\overline{\Omega})^m $.

中文翻译：

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具有更高质量耗散的二次反应扩散系统的时间一致边界

证明了在所有空间维度上反应扩散系统的非负经典解的时间一致界。假设系统耗散了总质量，并且具有至多（略超）二次增长的局部Lipschitz非线性。这推动了关于耗散质量的反应扩散系统的整体存在的最新进展，其中仅在一维或二维空间中知道了时间均匀边界。作为一种应用，偏斜对称的Lotka-Volterra系统显示出具有独特的经典解决方案，这些解决方案在各个维度上的时间均受时间限制，轨迹相对紧凑，为C（\ overline {\ Omega}）^ m $。