Differential and Integral Equations

Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type

Mikhail M. Lavrentiev and Renato Spigler

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Abstract

Time-independent bounds for the classical solutions of a certain nonlinear integroparabolic equation of the Fokker-Planck type are established. Such an equation describes the statistical time evolution of large populations of nonlinearly coupled random oscillators with inertia. The basic tool is deriving ``energy-like" estimates. A comparison theorem is also proved to obtain estimates for the solutions in terms of some special solutions.

Article information

Source
Differential Integral Equations Volume 17, Number 5-6 (2004), 549-570.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060347

Mathematical Reviews number (MathSciNet)
MR2054934

Zentralblatt MATH identifier
1174.35406

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc. 35K55: Nonlinear parabolic equations 35R10: Partial functional-differential equations 82C31: Stochastic methods (Fokker-Planck, Langevin, etc.) [See also 60H10]

Citation

Lavrentiev, Mikhail M.; Spigler, Renato. Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type. Differential Integral Equations 17 (2004), no. 5-6, 549--570. https://projecteuclid.org/euclid.die/1356060347.


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