Mixed problem for a nonlinear ultraparabolic equation that generalizes the diffusion equation with inertia

Abstract

We consider a mixed problem for a nonlinear ultraparabolic equation that is a nonlinear generalization of the diffusion equation with inertia and the special cases of which are the Fokker-Planck equation and the Kolmogorov equation. Conditions for the existence and uniqueness of a solution of this problem are established.