The Kuramoto-Sakaguchi (or simply Kuramoto) equation is considered when the ''frequency distribution'', the frequency being an independent variable in the model equation, has an 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 here established, taking suitable limits in the formulation of the previously studied problem, where the aforementioned support was assumed to be bounded.

LAVRENTIEV M. M., J.r., Spigler, R., Tani, A. (2014). Existence, uniqueness, and regularity for the Kuramoto-Sakaguchi equation with unboundedly supported frequency distribution. DIFFERENTIAL AND INTEGRAL EQUATIONS, 27(9-10), 879-892.

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

SPIGLER, Renato;
2014-01-01

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 an 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 here established, taking suitable limits in the formulation of the previously studied problem, where the aforementioned support was assumed to be bounded.
LAVRENTIEV M. M., J.r., Spigler, R., Tani, A. (2014). Existence, uniqueness, and regularity for the Kuramoto-Sakaguchi equation with unboundedly supported frequency distribution. DIFFERENTIAL AND INTEGRAL EQUATIONS, 27(9-10), 879-892.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/136859
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