用能量变分方法研究可逆Gray-Scott型系统及其不可逆极限
On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit
摘要：
以往对Gray-Scott模型的研究大多将其视为一个不可逆的化学反应体系。本文基于质量作用定律，利用能量变分方法导出了一类四种群反应扩散系统。这是一个可逆的Gray-Scott型模型，具有自然的熵结构。我们建立了该系统的局部适定性，并证明了当某些后向系数趋于零时，相应的不可逆Gray-Scott型系统的极限。进一步，在初始数据的小性假设下，我们得到了该可逆系统经典解的整体存在性。
英文摘要：
Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion system using the energetic variational approach based on the law of mass action. This is a reversible Gray-Scott type model, which has a natural entropy structure. We establish the local well-posedness of this system, and justify the limit to the corresponding irreversible Gray-Scott type system as some backward coefficients tend to zero. Furthermore, under some smallness assumption on the initial data, we obtain the global-in-time existence of classical solutions of the reversible system.
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