Global-in-time solution and stability of Kuramoto-Sakaguchi equation under non-local Coupling

Hirotada Honda

doi:10.3934/nhm.2017002

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2017, Volume 12, Issue 1: 25-57. Doi: 10.3934/nhm.2017002

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Global-in-time solution and stability of Kuramoto-Sakaguchi equation under non-local Coupling

Hirotada Honda

Midori-Cho 3-9-11, Musashino-Shi, Tokyo 180-8585, Japan

Received: April 30, 2016

Revised: August 31, 2016

Published: May 2017

We thank the anonymous referees for valuable comments to improve the quality of this paper.

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Abstract

In this paper, we focus on the global-in-time solvability of the Kuramoto-Sakaguchi equation under non-local coupling. We further study the nonlinear stability of the trivial stationary solution in the presence of sufficiently large diffusivity, and the existence of the solution under vanishing diffusion.

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Mathematics Subject Classification: Primary: 35B10, 35B41; Secondary: 35Q70.

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