Time-periodic linear boundary value problems on a finite interval

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2021-09-02 DOI:10.1090/qam/1615

A. S. Fokas, B. Pelloni, D. Smith

引用次数: 3

Abstract

We study the large time behaviour of the solution of a linear dispersive PDEs posed on a finite interval, when the prescribed boundary conditions are time periodic. We use the approach pioneered in [7] for nonlinear integrable PDEs. and then applied to linear problems on the half-line in [6], to characterise necessary conditions for the solution of such a problem to be periodic, at least in an asymptotic sense. We then fully describe the periodicity properties of the solution in three important illustrative examples, recovering known results for the second-order cases and establishing new ones for the third order one.

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有限区间上的时间周期线性边值问题

当规定的边界条件是时间周期性的时，我们研究了有限区间上线性色散偏微分方程解的大时间行为。对于非线性可积偏微分方程，我们使用[7]中开创的方法。然后应用于[6]中半线上的线性问题，至少在渐近意义上，刻画这种问题的解是周期性的必要条件。然后，我们在三个重要的示例中充分描述了解的周期性性质，恢复了二阶情况的已知结果，并建立了三阶情况的新结果。

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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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.