On the Krein-Rutman theorem and beyond
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908682374086656 |
|---|---|
| author | Sanchez, Claudia Fonte Gabriel, Pierre Mischler, Stéphane |
| author_facet | Sanchez, Claudia Fonte Gabriel, Pierre Mischler, Stéphane |
| contents | In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results with constructive estimates about: the existence of a solution to the first eigentriplet problem; the geometry of the principal eigenvalue problem; the asymptotic stability of the first eigenvector with possible constructive rate of convergence. This abstract theory is motivated and illustrated by several examples of differential, integro-differential and integral operators. In particular, we revisit the first eigenvalue problem and the asymptotic stability of the first eigenvector for: some parabolic equations in a bounded domain and in the whole space; some transport equations in a bounded or unbounded domain, including some growth-fragmentation models and some kinetic models; the kinetic Fokker-Planck equation in the torus and in the whole space; some mutation-selection models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06652 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the Krein-Rutman theorem and beyond Sanchez, Claudia Fonte Gabriel, Pierre Mischler, Stéphane Analysis of PDEs Functional Analysis Spectral Theory In this work, we revisit the Krein-Rutman theory for semigroups of positive operators in a Banach lattice framework and we provide some very general, efficient and handy results with constructive estimates about: the existence of a solution to the first eigentriplet problem; the geometry of the principal eigenvalue problem; the asymptotic stability of the first eigenvector with possible constructive rate of convergence. This abstract theory is motivated and illustrated by several examples of differential, integro-differential and integral operators. In particular, we revisit the first eigenvalue problem and the asymptotic stability of the first eigenvector for: some parabolic equations in a bounded domain and in the whole space; some transport equations in a bounded or unbounded domain, including some growth-fragmentation models and some kinetic models; the kinetic Fokker-Planck equation in the torus and in the whole space; some mutation-selection models. |
| title | On the Krein-Rutman theorem and beyond |
| topic | Analysis of PDEs Functional Analysis Spectral Theory |
| url | https://arxiv.org/abs/2305.06652 |