Differential and Integral Equations
- Differential Integral Equations
- Volume 13, Number 4-6 (2000), 649-667.
Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation
Global in time existence and uniqueness of classical solutions to a certain nonlinear parabolic partial differential equation, containing an integral term, are proved. Smoothness regularity and time-independent estimates for all partial derivatives are also obtained. Such an equation is of a non-standard type, and governs the time evolution of certain populations of infinitely many nonlinearly coupled random oscillators, described by a model first proposed by Kuramoto and Sakaguchi.
Differential Integral Equations, Volume 13, Number 4-6 (2000), 649-667.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B45: A priori estimates 35B65: Smoothness and regularity of solutions 35R10: Partial functional-differential equations 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Lavrentiev, Mikhail M.; Spigler, Renato. Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation. Differential Integral Equations 13 (2000), no. 4-6, 649--667. https://projecteuclid.org/euclid.die/1356061243