Differential and Integral Equations

Existence, uniqueness, and regularity for the Kuramoto--Sakaguchi equation with unboundedly supported frequency distribution

Mikhail M. Lavrentiev, Jr., Renato Spigler, and Atusi Tani

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 9/10 (2014), 879-892.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1404230049

Mathematical Reviews number (MathSciNet)
MR3229095

Zentralblatt MATH identifier
1298.26040

Subjects
Primary: 35K61: Nonlinear initial-boundary value problems for nonlinear parabolic equations 35K55: Nonlinear parabolic equations 35K20: Initial-boundary value problems for second-order parabolic equations 35K10: Second-order parabolic equations 35B65: Smoothness and regularity of solutions

Citation

Lavrentiev, Jr., Mikhail M.; Spigler, Renato; Tani, Atusi. Existence, uniqueness, and regularity for the Kuramoto--Sakaguchi equation with unboundedly supported frequency distribution. Differential Integral Equations 27 (2014), no. 9/10, 879--892. https://projecteuclid.org/euclid.die/1404230049


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