Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

Shuang Liu; Yuan Lou; Rui Peng; Maolin Zhou

doi:10.1090/proc/14653

Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

Shuang Liu, Yuan Lou, Rui Peng, Maolin Zhou

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

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 Poláčik.

Original language	English
Pages (from-to)	5291-5302
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	12
DOIs	https://doi.org/10.1090/proc/14653
Publication status	Published - 2019
Externally published	Yes

Keywords

Asymptotics
Frequency
Monotonicity
Principal eigenvalue
Time-periodic parabolic operator

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10.1090/proc/14653

Cite this

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title = "Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator",

abstract = "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 Pol{\'a}{\v c}ik.",

keywords = "Asymptotics, Frequency, Monotonicity, Principal eigenvalue, Time-periodic parabolic operator",

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AU - Liu, Shuang

AU - Lou, Yuan

AU - Peng, Rui

AU - Zhou, Maolin

PY - 2019

Y1 - 2019

N2 - 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 Poláčik.

AB - 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 Poláčik.

KW - Asymptotics

KW - Frequency

KW - Monotonicity

KW - Principal eigenvalue

KW - Time-periodic parabolic operator

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U2 - 10.1090/proc/14653

DO - 10.1090/proc/14653

M3 - Article

AN - SCOPUS:85074297458

SN - 0002-9939

VL - 147

SP - 5291

EP - 5302

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

Monotonicity of the principal eigenvalue for a linear time-periodic parabolic operator

Abstract

Keywords

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