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

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

Článek WoS

We study the spatially homogeneous granular medium equation partial derivative t mu=div(mu del V)+div(mu(del W & lowast;mu))+Delta mu,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t\mu =\textrm{div}(\mu \nabla V)+\textrm{div}(\mu (\nabla W *\mu ))+\Delta \mu \,, \end{aligned}$$\end{document}within a large and natural class of the confinement potentials V and interaction potentials W. The considered problem do not need to assume that del V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla V$$\end{document} or del W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla W$$\end{document} 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.

We study the spatially homogeneous granular medium equation partial derivative t mu=div(mu del V)+div(mu(del W & lowast;mu))+Delta mu,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \partial _t\mu =\textrm{div}(\mu \nabla V)+\textrm{div}(\mu (\nabla W *\mu ))+\Delta \mu \,, \end{aligned}$$\end{document}within a large and natural class of the confinement potentials V and interaction potentials W. The considered problem do not need to assume that del V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla V$$\end{document} or del W\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\nabla W$$\end{document} 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.

Particle approximation, Gradient flows, Wasserstein metric

Particle approximation, Gradient flows, Wasserstein metric

BENKO, M.; CHLEBICKA, I.; ENDAL, J.; MIASOJEDOW, B.

19.03.2026

Springer Nature

NUMERISCHE MATHEMATIK

158

Spolková republika Německo

411

454

44

https://link.springer.com/article/10.1007/s00211-025-01516-0