تقرير
On the Krein-Rutman theorem and beyond
| العنوان: | On the Krein-Rutman theorem and beyond |
|---|---|
| المؤلفون: | Fonte Sanchez, Claudia, Gabriel, Pierre, Mischler, Stéphane |
| المساهمون: | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), ANR-20-CE40-0015,NOLO,Processus de branchement non-locaux(2020), European Project |
| المصدر: | https://hal.science/hal-04093201Test ; 2023. |
| بيانات النشر: | HAL CCSD |
| سنة النشر: | 2023 |
| المجموعة: | Université de Versailles Saint-Quentin-en-Yvelines: HAL-UVSQ |
| مصطلحات موضوعية: | [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP], [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] |
| الوصف: | 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, intro-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-fragmentationmodels and some kinetic models;- the kinetic Fokker-Planck equation in the torus and in the whole space;- some mutation-selection models. |
| نوع الوثيقة: | report |
| اللغة: | English |
| العلاقة: | info:eu-repo/semantics/altIdentifier/arxiv/2305.06652; hal-04093201; https://hal.science/hal-04093201Test; https://hal.science/hal-04093201/documentTest; https://hal.science/hal-04093201/file/FSGM-KR-v1.pdfTest; ARXIV: 2305.06652 |
| الإتاحة: | https://hal.science/hal-04093201Test https://hal.science/hal-04093201/documentTest https://hal.science/hal-04093201/file/FSGM-KR-v1.pdfTest |
| حقوق: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.5BD66E82 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |