On a reversible Gray-Scott type system from energetic variational approach and its irreversible limit

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

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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 solution of the reversible system.

Original languageEnglish (US)
Pages (from-to)427-454
Number of pages28
JournalJournal of Differential Equations
StatePublished - Feb 5 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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