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Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type. (English) Zbl 1174.35406
Summary: 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.
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35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
45K05 Integro-partial differential equations