一些具有大平流的非自交算子扩散率主特征值的非单调性

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED SIAM Journal on Mathematical Analysis Pub Date : 2024-09-03 DOI:10.1137/23m1603947

Shuang Liu

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 5 期，第 6025-6056 页，2024 年 10 月。摘要本文关注两类非自相加算子的主特征值关于扩散率的单调性：时周期抛物线算子和具有剪切流的椭圆算子。当频率或流动振幅（称为平流率）足够大时，这些算子的行为类似于某些平均自相交椭圆算子。S. Liu 和 Y. Lou，J. Funct. Anal.，282 (2022), 109338]中猜想，在大平流情况下，主特征值在扩散率上是单调的，这与那些自相关椭圆算子类似。我们通过建立主特征值在足够大的扩散率和平流率下的高阶展开，为猜想提供了一些反例。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonmonotonicity of Principal Eigenvalues in Diffusion Rate for Some Non-Self-Adjoint Operators with Large Advection

SIAM Journal on Mathematical Analysis, Volume 56, Issue 5, Page 6025-6056, October 2024.
Abstract. The paper is concerned with the monotonicity of the principal eigenvalues with respect to diffusion rate for two classes of non-self-adjoint operators: time-periodic parabolic operators and elliptic operators with shear flow. These operators behave similarly to some averaged self-adjoint elliptic operators when the frequency or flow amplitude, referred to as advection rate, is sufficiently large. It was conjectured in [S. Liu and Y. Lou, J. Funct. Anal., 282 (2022), 109338] that the principal eigenvalues are monotone in diffusion rate for large advection, similarly to those self-adjoint elliptic operators. We provide some counterexamples to the conjecture by establishing the high order expansion of the principal eigenvalues for sufficiently large diffusion and advection rates.

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.