TY - JOUR
T1 - On a reversible Gray-Scott type system from energetic variational approach and its irreversible limit
AU - Liang, Jiangyan
AU - Jiang, Ning
AU - Liu, Chun
AU - Wang, Yiwei
AU - Zhang, Teng Fei
N1 - Funding Information:
This work is partially supported by the National Science Foundation (USA) grants NSF DMS-1759536 , NSF DMS-1950868 , the United States-Israel Binational Science Foundation (BSF) # 2024246 (C. Liu, Y. Wang), the grants from the National Natural Science Foundation of China No. 11971360 and No. 11731008 (N. Jiang), and No. 11871203 (T.-F. Zhang), and the Strategic Priority Research Program of Chinese Academy of Sciences under Grant No. XDA25010404 (N. Jiang). This work was initiated when T.-F. Zhang visited the Department of Applied Mathematics at Illinois Institute of Technology, he would like to acknowledge the hospitality of IIT and the sponsorship of the China Scholarship Council , under the State Scholarship Fund No. 201906415023 . The authors are very grateful to the anonymous referees for their valuable comments and suggestions.
Publisher Copyright:
© 2021 Elsevier Inc.
PY - 2022/2/5
Y1 - 2022/2/5
N2 - 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.
AB - 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.
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U2 - 10.1016/j.jde.2021.11.032
DO - 10.1016/j.jde.2021.11.032
M3 - Article
AN - SCOPUS:85120423026
SN - 0022-0396
VL - 309
SP - 427
EP - 454
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -