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A GLOBAL WELL-POSEDNESS AND ASYMPTOTIC DYNAMICS OF THE KINETIC WINFREE EQUATION
- Authors
- Ha, Seung-Yeal; Park, Jinyeong; Zhang, Xiongtao
- Issue Date
- Apr-2020
- Publisher
- AMER INST MATHEMATICAL SCIENCES-AIMS
- Keywords
- Mean-field limit; measure-valued solution; synchronization; the Win-free model; asymptotic behavior
- Citation
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, v.25, no.4, pp.1317 - 1344
- Indexed
- SCIE
SCOPUS
- Journal Title
- DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
- Volume
- 25
- Number
- 4
- Start Page
- 1317
- End Page
- 1344
- ISSN
- 1531-3492
- 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.
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Related Researcher
- Park, Jin yeong
- COLLEGE OF NATURAL SCIENCES (DEPARTMENT OF MATHEMATICS)