A Trotter product formula for gradient flows in metric spaces
Philippe Cl\'ement, Jan Maas
TL;DR
This paper proves a Trotter product formula for gradient flows in metric spaces and applies it to demonstrate convergence of splitting methods for certain Fokker-Planck and porous medium equations with potentials.
Contribution
The paper introduces a Trotter product formula for gradient flows in metric spaces and uses it to analyze convergence of splitting methods for complex PDEs.
Findings
Established a Trotter product formula for gradient flows in metric spaces.
Proved convergence of splitting methods for Fokker-Planck and porous medium equations.
Applied the formula to equations perturbed by potentials.
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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations · Geometry and complex manifolds