Differential and Integral Equations
- Differential Integral Equations
- Volume 27, Number 9/10 (2014), 879-892.
Existence, uniqueness, and regularity for the Kuramoto--Sakaguchi equation with unboundedly supported frequency distribution
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.
Differential Integral Equations, Volume 27, Number 9/10 (2014), 879-892.
First available in Project Euclid: 1 July 2014
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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