Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling
Analysis of PDEs
2025-03-03 v2 Numerical Analysis
Numerical Analysis
Abstract
This paper is concerned with the problem of counting solutions of stationary nonlinear Partial Differential Equations (PDEs) when the PDE is known to admit more than one solution. We suggest tackling the problem via a sampling-based approach. We test our proposed methodology on the McKean-Vlasov PDE, more precisely on the problem of determining the number of stationary solutions of the McKean-Vlasov (or porous medium) equation.
Keywords
Cite
@article{arxiv.2411.07390,
title = {Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling},
author = {Martin Kolodziejczyk and Michela Ottobre and Gideon Simpson},
journal= {arXiv preprint arXiv:2411.07390},
year = {2025}
}