Convergence of a linearly transformed particle method for aggregation equations

Convergence of a linearly transformed particle method for aggregation equations

We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the regularity of the initial data. Moreover, we give convergence es...

Full description

Saved in:
Bibliographic Details
Main Authors: Pinto, Martin Campos, Carrillo, José A, Charles, Frédérique, Choi, Young-Pil
Format: Journal Article
Language:English
Published: 27-07-2015
Subjects:
Mathematics - Numerical Analysis
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in $L^1 \cap L^p$ norm.
DOI:10.48550/arxiv.1507.07405