MONOTONICITY OF THE PRINCIPAL EIGENVALUE FOR A LINEAR TIME-PERIODIC PARABOLIC OPERATOR

被引：20

作者：

Liu, Shuang ^{[1
]}

Lou, Yuan ^{[2
]}

Peng, Rui ^{[3
]}

Zhou, Maolin ^{[4
]}

机构：

[1] Renmin Univ China, Inst Math Sci, Beijing 100872, Peoples R China

[2] Ohio State Univ, Dept Math, 231 W 18th Ave, Columbus, OH 43210 USA

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[4] Univ New England, Sch Sci & Technol, Dept Math, Armidale, NSW 2341, Australia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 12期

基金：

澳大利亚研究理事会; 美国国家科学基金会;

关键词：

Time-periodic parabolic operator; principal eigenvalue; frequency; monotonicity; asymptotics; ELLIPTIC OPERATOR; ADVECTION; DIFFUSION;

D O I：

10.1090/proc/14653

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the effect of frequency on the principal eigenvalue of a time-periodic parabolic operator with Dirichlet, Robin, or Neumann boundary conditions. The monotonicity and asymptotic behaviors of the principal eigenvalue with respect to the frequency parameter are established. Our results prove a conjecture raised by Hutson, Michaikow, and Polacik.

引用

页码：5291 / 5302

页数：12

共 13 条

[1] Elliptic eigenvalue problems with large drift and applications to nonlinear propagation phenomena
Berestycki, H
Hamel, F
Nadirashvili, N
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2005, 253 (02) : 451 - 480
[2] Cantrell Robert Stephen, 2003, WILEY SERIES MATH CO, DOI 10.1002/0470871296
[3] Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model
Chen, Xinfu
Lou, Yuan
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2008, 57 (02) : 627 - 658
[4] Effects of Diffusion and Advection on the Smallest Eigenvalue of an Elliptic Operator and Their Applications
Chen, Xinfu
Lou, Yuan
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2012, 61 (01) : 45 - 80
[5] HESS P., 1991, PITMAN RES NOTES MAT, V247
[6] The evolution of dispersal rates in a heterogeneous time-periodic environment
Hutson, V
Mischaikow, K
Polácik, P
[J]. JOURNAL OF MATHEMATICAL BIOLOGY, 2001, 43 (06) : 501 - 533
[7] Estimates for the principal spectrum point for certain time-dependent parabolic operators
Hutson, V
Shen, W
Vickers, GT
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (06) : 1669 - 1679
[8] Liu S., 2018, FUNCTIONAL APP UNPUB
[9] The principal eigenvalue of a space-time periodic parabolic operator
Nadin, Gregoire
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2009, 188 (02) : 269 - 295
[10] Ni WM, 2011, CBMS-NSF MA, V82, P1, DOI 10.1137/1.9781611971972

← 1 2 →