Work

Convergence rates of particle approximation of forward-backward splitting algorithm for granular medium equations

Year: 2026

Type: article

Abstract: We study the spatially homogeneous granular medium equation $$\begin{aligned} \partial _t\mu =\textrm{div}(\mu \nabla V)+\textrm{div}(\mu (\nabla W *\mu ))+\Delta \mu \,, \end{aligned}$$ ∂ t μ = div ( μ ∇ V ) + div ( μ ( ∇ W ∗ μ ) ) + Δ μ , within a large and natural class of the confinement potentials V and interaction potentials W . The considered problem do not need to assume that $$\nabla V$$ ∇ V or $$\nabla W$$ ∇ W are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.

Source: Numerische Mathematik

DOI: 10.1007/s00211-025-01516-0

Authors: Matej Benko, Iwona Chlebicka, Jørgen Endal, Błażej Miasojedow

Institutions: Brno University of Technology, University of Warsaw, Norwegian University of Science and Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190