Time-independent estimates and a comparison theorem for a nonlinear integroparabolic equation of the Fokker-Planck type. (English) Zbl 1174.35406

Lavrentiev, Mikhail M.; Spigler, Renato

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