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

Martin Kolodziejczyk; Michela Ottobre; Gideon Simpson

doi:10.48550/arxiv.2411.07390

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

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

Martin Kolodziejczyk, Michela Ottobre and Gideon Simpson

11 Nov 2024

DOI: https://doi.org/10.48550/arxiv.2411.07390

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Abstract

Computer Science - Numerical Analysis

Mathematics - Analysis of PDEs

Mathematics - Numerical Analysis

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.

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Title: Counting the number of stationary solutions of Partial Differential Equations via infinite dimensional sampling
Creators: Martin Kolodziejczyk
Michela Ottobre
Gideon Simpson
Resource Type: Preprint
Language: English
Academic Unit: Mathematics
Other Identifier: 991021959915404721

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

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Abstract

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