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arXiv · 1510.04020

Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biaising force processes

Houssam Alrachid·Tony Lelièvre·Raafat Talhouk
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Abstract

We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non- linear term is related to a conditional expectation, and is thus non-local. The proof uses tools from the theory of semigroups of linear operators for the local existence result, and an a priori estimate based on a supersolution for the global existence result.

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Houssam Alrachid, Tony Lelièvre, Raafat Talhouk. 2015-10-14. Local and global solution for a nonlocal Fokker-Planck equation related to the adaptive biaising force processes. https://arxiv.org/abs/1510.04020

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