Notes on a Wasserstein metric convergence method for Fokker-Planck equations with point controls

Luca Petrelli
Department of Mathematical Sciences
Carnegie Mellon University, Pittsburgh, PA 15213
luca@andrew.cmu.edu

Abstract: We employ the Monge-Kantorovich mass transfer theory to obtain an existence and uniqueness result for Fokker-Planck Equations with time dependent point control. We prove existence for an approximate problem and then show convergence in the Wasserstein distance through equivalence with weak-$\star$ convergence.

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