Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling

Fuente: arXiv
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Main Authors: Kolodziejczyk, Martin, Ottobre, Michela, Simpson, Gideon
Format: Preprint
Published: 2024
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_version_ 1866915176223080448
author Kolodziejczyk, Martin
Ottobre, Michela
Simpson, Gideon
author_facet Kolodziejczyk, Martin
Ottobre, Michela
Simpson, Gideon
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_07390
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling
Kolodziejczyk, Martin
Ottobre, Michela
Simpson, Gideon
Analysis of PDEs
Numerical Analysis
35Q83, 35Q70, 60H15, 65M22, 65K99, 82M60
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.
title Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling
topic Analysis of PDEs
Numerical Analysis
35Q83, 35Q70, 60H15, 65M22, 65K99, 82M60
url https://arxiv.org/abs/2411.07390