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Journal of Evolution Equations

, Volume 11, Issue 2, pp 405–427 | Cite as

A Trotter product formula for gradient flows in metric spaces

  • Philippe Clément
  • Jan Maas
Open Access
Article

Abstract

We prove a Trotter product formula for gradient flows in metric spaces. This result is applied to establish convergence in the L 2-Wasserstein metric of the splitting method for some Fokker-Planck equations and porous medium type equations perturbed by a potential.

Mathematics Subject Classification (2000)

Primary 49Q20 Secondary 35A15 47H20 82C31 

Keywords

Gradient flows Trotter product formula splitting method Fokker Planck equations 

Notes

Acknowledgment

We are grateful to the anonymous referee for his useful remarks.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2011

Authors and Affiliations

  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.Institute for Applied MathematicsUniversity of BonnBonnGermany

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