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

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.