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arXiv · 1206.2673

Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space

Hwa Kil Kim
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Abstract

In this paper, we study the stability property of Hamiltonian systems on the Wasserstein space. Let $H$ be a given Hamiltonian satisfying certain properties. We regularize $H$ using the Moreau-Yosida approximation and denote it by $H_τ.$ We show that solutions of the Hamiltonian system for $H_τ$ converge to a solution of the Hamiltonian system for $H$ as $τ$ converges to zero. We provide sufficient conditions on $H$ to carry out this process.

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Hwa Kil Kim. 2012-06-12. Moreau-Yosida approximation and convergence of Hamiltonian systems on Wasserstein space. https://arxiv.org/abs/1206.2673

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