5 papers
Fokker-Planck-Kolmogorov inclusions of the mean field type
Yurii Averboukh
The paper studies a dynamical system in the Wasserstein space, where the evolution is governed by a Fokker-Planck-Kolmogorov equation with coefficients chosen from a prescribed set…
Proximal aiming in weak KAM theory with nonsmooth Lagrangian
Yurii Averboukh
This work extends weak KAM theory to the case of a nonsmooth Lagrangian satisfying a superlinear growth condition. Using the solution of a weak KAM equation that is a stationary Ha…
Upper and lower bounds of the value function for optimal control in the Wasserstein space
Yurii Averboukh, Aleksei Volkov
This paper explores the application of nonsmooth analysis in the Wasserstein space to finite-horizon optimal control problems for nonlocal continuity equations. We characterize the…
Time-optimal problem in the space of probabilities measures
Yurii Averboukh, Ekaterina Kolpakova
This paper focuses on the value function in the time-optimal problem for a continuity equation in the space of probability measures. We derive the dynamic programming principle for…
Continuous time Markov chain based approximation of stationary and weak KAM Hamilton-Jacobi equations
Yurii Averboukh
Main objects of the paper are stationary and weak KAM Hamilton-Jacobi equations on the finite-dimensional torus. The key idea of the paper is to replace the underlying calculus of…