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On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit by Liang, Jiangyan; Jiang, Ning; Liu, Chun; Wang, Yiwei; Zhang, Teng-Fei is a scholarly article available to read on EtoBox.

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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.

Author

Liang, Jiangyan; Jiang, Ning; Liu, Chun; Wang, Yiwei; Zhang, Teng-Fei

Published

2021

Language

EN