Translator Disclaimer
September/October 2014 Existence, uniqueness, and regularity for the Kuramoto--Sakaguchi equation with unboundedly supported frequency distribution
Mikhail M. Lavrentiev, Jr., Renato Spigler, Atusi Tani
Differential Integral Equations 27(9/10): 879-892 (September/October 2014).

Abstract

The Kuramoto-Sakaguchi (or simply Kuramoto) equation is considered when the "frequency distribution", the frequency being an independent variable in the model equation, has unbounded support. This equation is a nonlinear, Fokker-Planck-type, parabolic integro-differential equation, and arises from the statistical description of the dynamical behavior of populations of infinitely many nonlinearly coupled random oscillators. The space-integral term in the equation accounts for mean-field interaction occurring among these oscillators. Existence, uniqueness, and regularity of solutions are established here, taking suitable limits in the formulation of the previously studied problem, where the aforementioned support was assumed to be bounded.

Citation

Download Citation

Mikhail M. Lavrentiev, Jr.. Renato Spigler. Atusi Tani. "Existence, uniqueness, and regularity for the Kuramoto--Sakaguchi equation with unboundedly supported frequency distribution." Differential Integral Equations 27 (9/10) 879 - 892, September/October 2014.

Information

Published: September/October 2014
First available in Project Euclid: 1 July 2014

zbMATH: 1298.26040
MathSciNet: MR3229095

Subjects:
Primary: 35B65, 35K10, 35K20, 35K55, 35K61

Rights: Copyright © 2014 Khayyam Publishing, Inc.

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.27 • No. 9/10 • September/October 2014
Back to Top