Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _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 |