Deterministic particle method for nonlinear nonlocal scalar balance equations
Analysis of PDEs
2024-11-13 v2 Numerical Analysis
Numerical Analysis
Abstract
We study a deterministic particle scheme to solve a scalar balance equation with nonlocal interaction and nonlinear mobility used to model congested dynamics. The main novelty with respect to "Radici-Stra [SIAM J. Math. Anal. 55.3 (2023)]" is the presence of a source term; this causes the solutions to no longer be probability measures, thus requiring a suitable adaptation of the numerical scheme and of the estimates leading to compactness.
Cite
@article{arxiv.2411.07148,
title = {Deterministic particle method for nonlinear nonlocal scalar balance equations},
author = {Emanuela Radici and Federico Stra},
journal= {arXiv preprint arXiv:2411.07148},
year = {2024}
}
Comments
26 pages, 1 figure