Differential and Integral Equations

Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation

Mikhail M. Lavrentiev and Renato Spigler

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Abstract

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.

Article information

Source
Differential Integral Equations Volume 13, Number 4-6 (2000), 649-667.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356061243

Mathematical Reviews number (MathSciNet)
MR1750044

Zentralblatt MATH identifier
0997.35029

Subjects
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]

Citation

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.


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