Lavrentiev, Mikhail M.; Spigler, Renato Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type. (English) Zbl 1174.35406 Differ. Integral Equ. 17, No. 5-6, 549-570 (2004). 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. MSC: 35K20 Initial-boundary value problems for second-order parabolic equations 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 45K05 Integro-partial differential equations Keywords:nonlinear integroparabolic equation; Fokker-Planck type; time-independent bound PDF BibTeX XML Cite \textit{M. M. Lavrentiev} and \textit{R. Spigler}, Differ. Integral Equ. 17, No. 5--6, 549--570 (2004; Zbl 1174.35406)