Hopf-Cole transformation via generalized Schr\"odinger bridge problem
Dynamical Systems
2019-01-29 v1 Analysis of PDEs
Optimization and Control
Abstract
We study generalized Hopf-Cole transformations motivated by the Schr\"odinger bridge problem, which can be seen as a boundary value Hamiltonian system on the Wasserstein space. We prove that generalized Hopf-Cole transformations are symplectic submersions in the Wasserstein symplectic geometry. Many examples, including a Hopf-Cole transformation for the shallow water equations, are given. Based on this transformation, energy splitting inequalities are provided.
Cite
@article{arxiv.1901.09051,
title = {Hopf-Cole transformation via generalized Schr\"odinger bridge problem},
author = {Flavien Léger and Wuchen Li},
journal= {arXiv preprint arXiv:1901.09051},
year = {2019}
}