Estimates for Kantorovich functionals between solutions to Fokker -- Planck -- Kolmogorov equations with dissipative drifts

TL;DR

This paper derives estimates for Kantorovich functionals between solutions of Fokker-Planck-Kolmogorov equations with varying drifts, aiding in understanding their well-posedness and stability.

Contribution

It provides new bounds for Kantorovich functionals between solutions with different drifts, extending the analysis of Fokker-Planck-Kolmogorov equations.

Findings

Estimates for Kantorovich functionals between solutions with different drifts

Applications to well-posedness of nonlinear equations

Analysis of solutions with same diffusion but varying drifts

Abstract

We obtain estimates for the Kantorovich functionals between solutions to different Fokker -- Planck -- Kolmogorov equations for measures with same diffusion part but different drifts and different initial conditions. We show possible applications of such estimates to the study of the well-posedness for nonlinear equations.