A Trotter product formula for gradient flows in metric spaces. (English) Zbl 1232.49051
Summary: 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.
MSC:
| 49Q20 | Variational problems in a geometric measure-theoretic setting |
| 35A15 | Variational methods applied to PDEs |
| 47H20 | Semigroups of nonlinear operators |
| 82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
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