A GLOBAL WELL-POSEDNESS AND ASYMPTOTIC DYNAMICS OF THE KINETIC WINFREE EQUATION
- Title
- A GLOBAL WELL-POSEDNESS AND ASYMPTOTIC DYNAMICS OF THE KINETIC WINFREE EQUATION
- Author
- 박진영
- Keywords
- Mean-field limit; measure-valued solution; synchronization; the Win-free model; asymptotic behavior
- Issue Date
- 2020-04
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v. 25, no. 4, page. 1317-1344
- Abstract
- We study a global well-posedness and asymptotic dynamics of measure-valued solutions to the kinetic Winfree equation. For this, we introduce a second-order extension of the first-order Winfree model on an extended phase-frequency space. We present the uniform(-in-time) l(p)-stability estimate with respect to initial data and the equivalence relation between the original Winfree model and its second-order extension. For this extended model, we present uniform-in-time mean-field limit and large-time behavior of measure-valued solution for the second-order Winfree model. Using stability and asymptotic estimates for the extended model and the equivalence relation, we recover the uniform mean-field limit and large-time asymptotics for the Winfree model. 200 words.
- URI
- http://www.aimsciences.org/article/doi/10.3934/dcdsb.2019229https://repository.hanyang.ac.kr/handle/20.500.11754/166135
- ISSN
- 1531-3492; 1553-524X
- DOI
- 10.3934/dcdsb.2019229
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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