On the Limit of some Diffusion-Reaction System with Small Parameter

Gajewski, H.; Sparing, H.-D.

doi:10.4171/zaa/123

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2021

2022

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Cited by 2 publications

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“…Notice that more phenomena will arise when we consider different timescales for different reaction schemes in the (Re-GS) system. The limit issues of some diffusion-reaction system with small parameter are proved by Evans [9] and Gajewski-Sparing [11]. Chen-Gao [2] considered the well-posedness of a free boundary problem arising from the limit of a FitzHugh-Nagumo system (a slow-diffusion fast-reaction system).…”

Section: Introductionmentioning

confidence: 99%

On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit

Liang,

Jiang,

Liu

et al. 2021

Preprint

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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 reactiondiffusion 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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Section: Introductionmentioning

confidence: 99%