Seung‐Yeal Ha, Myeongju Kang, Hansol Park, T. Ruggeri, Woojoo Shim
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引用次数: 0
Abstract
We consider the thermodynamic Kuramoto model proposed in \cite{H-P-R-S}. For each oscillator in thermodynamic Kuramoto model, there is a coupling effect between the phase and the temperature field. For such a model, we study a uniform stability and uniform-in-time mean-field limit to the corresponding kinetic equation. For this, we first derive a uniform
ℓ
p
\ell ^p
-stability of the thermodynamic Kuramoto model with respect to initial data by directly estimating the temporal evolution of
ℓ
p
\ell ^p
-distance between two admissible solutions to the particle thermodynamic Kuramoto model. In a large-oscillator limit, the Vlasov type mean-field equation can be rigorously derived using the BBGKY hierarchy, uniform stability estimate, and particle-in-cell method. We construct unique global-in-time measure-valued solutions to the derived kinetic equation and also derive a uniform-in-time stability estimate and emergent estimates.
期刊介绍:
The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume.
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