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2000 Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation
Mikhail M. Lavrentiev Jr., Renato Spigler
Differential Integral Equations 13(4-6): 649-667 (2000).

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.

Citation

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Mikhail M. Lavrentiev Jr.. Renato Spigler. "Existence and uniqueness of solutions to the Kuramoto-Sakaguchi nonlinear parabolic integrodifferential equation." Differential Integral Equations 13 (4-6) 649 - 667, 2000.

Information

Published: 2000
First available in Project Euclid: 21 December 2012

zbMATH: 0997.35029
MathSciNet: MR1750044

Subjects:
Primary: 35K55
Secondary: 35B45, 35B65, 35R10, 45K05

Rights: Copyright © 2000 Khayyam Publishing, Inc.

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Vol.13 • No. 4-6 • 2000
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