Preprints, Working Papers, ... (Preprint) Year : 2024

On the Krein-Rutman theorem and beyond

Abstract

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.
Fichier principal
Vignette du fichier
FSGM-KR-v2.pdf (2.5 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-04093201 , version 1 (09-05-2023)
hal-04093201 , version 2 (10-01-2024)

Licence

Identifiers

Cite

Claudia Fonte Sánchez, Pierre Gabriel, Stéphane Mischler. On the Krein-Rutman theorem and beyond. 2024. ⟨hal-04093201v2⟩
435 View
273 Download

Altmetric

Share

More