Principal eigenvalue for some elliptic operators with large drift: Neumann boundary conditions

Autor:	Liu, Shuang, Lou, Yuan, Zhou, Maolin
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35P15 35P20 34C25
Druh dokumentu:	Working Paper
Popis:	The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate approaches infinity. Under some non-degeneracy assumptions, our results illustrate that these asymptotic behaviors are completely determined by some connected components in the omega-limit set of the system of ordinary differential equations associated with the drift term, which includes stable fixed points, stable limit cycles, hyperbolic saddles connecting homoclinic orbits, and families of closed orbits. Some discussions on degenerate cases are also included. Comment: 53 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.09031 Zobrazit plný text záznamu View this record from Arxiv