Journal article
Counting the number of stationary solutions of partial differential equations via infinite dimensional sampling
Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, v 383(2298), 20240239
05 Jun 2025
PMID: 40471034
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. The method allows one to find solutions that are stable, in the sense that they are stable equilibria of the associated time-dependent PDE. 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 equation.
This article is part of the theme issue ‘Partial differential equations in data science’.
Metrics
3 Record Views
Details
- Title
- Counting the number of stationary solutions of partial differential equations via infinite dimensional sampling
- Creators
- Martin Kolodziejczyk - Politecnico di MilanoMichela Ottobre (Corresponding Author) - Heriot-Watt UniversityGideon Simpson - Drexel University
- Publication Details
- Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, v 383(2298), 20240239
- Publisher
- The Royal Society
- Number of pages
- 16
- Grant note
- Ministero dell'Università e della Ricerca (http://dx.doi.org/10.13039/501100021856) EPSRC United States National Science Foundation Royal Society of Edinburgh (http://dx.doi.org/10.13039/501100000332)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:001508526700004
- Scopus ID
- 2-s2.0-105007656479
- Other Identifier
- 991022055079804721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Multidisciplinary Sciences