论文标题
一维反应扩散系统的非浓度现象与质量耗散
Non-concentration phenomenon for one dimensional reaction-diffusion systems with mass dissipation
论文作者
论文摘要
当非线性具有超二次生长速率时，已知具有质量耗散的反应扩散系统具有高度的爆炸溶液。在维度上，最近已经显示，如果非线性最多是立方体，则可以具有全球界面解决方案的存在。对于立方中间总和条件，即非线性可能具有任意高增长率，必须施加额外的熵不平等。在本文中，我们完全删除了此额外的熵假设，并获得具有立方中间总和条件的反应扩散系统的全局界限。新颖的想法是在质量耗散系统中显示出一种非集中现象，这就是质量耗散，这意味着在莫雷空间中的耗散$ \ mathsf {m}^{1，δ}（ω}（ω）$对于某些$ guex> 0 $。就我们而言，这是第一次为质量消散反应扩散系统得出这种界限。然后将结果应用于获得全球存在和解决方案对振荡性Belousov-Zhabotinskinky系统的界定，该系统满足了立方中间总和条件，但不能满足熵假设。扩展包括具有略微少数立方中间总和条件的全球存在质量控制系统。
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension one, it has been shown recently that one can have global existence of bounded solutions if nonlinearities are at most cubic. For the cubic intermediate sum condition, i.e. nonlinearities might have arbitrarily high growth rates, an additional entropy inequality had to be imposed. In this article, we remove this extra entropy assumption completely and obtain global boundedness for reaction-diffusion systems with cubic intermediate sum condition. The novel idea is to show a non-concentration phenomenon for mass dissipating systems, that is the mass dissipation implies a dissipation in a Morrey space $\mathsf{M}^{1,δ}(Ω)$ for some $δ>0$. As far as we are concerned, it is the first time such a bound is derived for mass dissipating reaction-diffusion systems. The results are then applied to obtain global existence and boundedness of solutions to an oscillatory Belousov-Zhabotinsky system, which satisfies cubic intermediate sum condition but does not fulfill the entropy assumption. Extensions include global existence mass controlled systems with slightly-super cubic intermediate sum condition.
