A global well-posedness and asymptotic dynamics of the kinetic Winfree equation | Zendy

Seung-Yeal Ha | Zendy; Jinyeong Park | Zendy; Xiongtao Zhang | Zendy

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A global well-posedness and asymptotic dynamics of the kinetic Winfree equation

Author(s) -

Seung-Yeal Ha,

Jinyeong Park,

Xiongtao Zhang

Publication year - 2019

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2019229

Subject(s) - equivalence (formal languages) , mathematics , limit (mathematics) , stability (learning theory) , extension (predicate logic) , measure (data warehouse) , space (punctuation) , field (mathematics) , statistical physics , mathematical analysis , pure mathematics , physics , computer science , database , machine learning , programming language , operating system

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) \begin{document}$ \ell_p $\end{document} -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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