广义本雅明方程解析半径的演化

IF 1.1 3区数学 Q1 MATHEMATICS Discrete and Continuous Dynamical Systems Pub Date : 2022-12-19 DOI:10.3934/dcds.2023039

Renata O. Figueira, M. Panthee

{"title":"广义本雅明方程解析半径的演化","authors":"Renata O. Figueira, M. Panthee","doi":"10.3934/dcds.2023039","DOIUrl":null,"url":null,"abstract":"In this work we consider the initial value problem for the generalized Benjamin equation \\begin{equation}\\label{Benj-IVP} \\begin{cases} \\partial_t u-l\\mathcal{H} \\partial_x^2u-\\partial_x^3u+u^p\\partial_xu = 0, \\quad x,\\; t\\in \\mathbb{R};\\;\\;,\\; p\\geq 1, \\\\ u(x,0) = u_0(x), \\end{cases} \\end{equation} where $u=u(x,t)$ is a real valued function, $0<l<1$ and $\\mathcal{H}$ is the Hilbert transform. This model was introduced by T. B. Benjamin (J. Fluid Mech. 245 (1992) 401--411) and describes unidirectional propagation of long waves in a two-fluid system where the lower fluid with greater density is infinitely deep and the interface is subject to capillarity. We prove that the local solution to the IVP associated with the generalized Benjamin equation for given data in the spaces of functions analytic on a strip around the real axis continue to be analytic without shrinking the width of the strip in time. We also study the evolution in time of the radius of spatial analyticity and show that it can decrease as the time advances. Finally, we present an algebraic lower bound on the possible rate of decrease in time of the uniform radius of spatial analyticity.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Evolution of the radius of analyticity for the generalized Benjamin equation\",\"authors\":\"Renata O. Figueira, M. Panthee\",\"doi\":\"10.3934/dcds.2023039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work we consider the initial value problem for the generalized Benjamin equation \\\\begin{equation}\\\\label{Benj-IVP} \\\\begin{cases} \\\\partial_t u-l\\\\mathcal{H} \\\\partial_x^2u-\\\\partial_x^3u+u^p\\\\partial_xu = 0, \\\\quad x,\\\\; t\\\\in \\\\mathbb{R};\\\\;\\\\;,\\\\; p\\\\geq 1, \\\\\\\\ u(x,0) = u_0(x), \\\\end{cases} \\\\end{equation} where $u=u(x,t)$ is a real valued function, $0<l<1$ and $\\\\mathcal{H}$ is the Hilbert transform. This model was introduced by T. B. Benjamin (J. Fluid Mech. 245 (1992) 401--411) and describes unidirectional propagation of long waves in a two-fluid system where the lower fluid with greater density is infinitely deep and the interface is subject to capillarity. We prove that the local solution to the IVP associated with the generalized Benjamin equation for given data in the spaces of functions analytic on a strip around the real axis continue to be analytic without shrinking the width of the strip in time. We also study the evolution in time of the radius of spatial analyticity and show that it can decrease as the time advances. Finally, we present an algebraic lower bound on the possible rate of decrease in time of the uniform radius of spatial analyticity.\",\"PeriodicalId\":51007,\"journal\":{\"name\":\"Discrete and Continuous Dynamical Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete and Continuous Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/dcds.2023039\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete and Continuous Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/dcds.2023039","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文研究广义本杰明方程\begin{equation}\label{Benj-IVP} \begin{cases} \partial_t u-l\mathcal{H} \partial_x^2u-\partial_x^3u+u^p\partial_xu = 0, \quad x,\; t\in \mathbb{R};\;\;,\; p\geq 1, \\ u(x,0) = u_0(x), \end{cases} \end{equation}的初值问题，其中$u=u(x,t)$为实值函数，$0本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Evolution of the radius of analyticity for the generalized Benjamin equation

In this work we consider the initial value problem for the generalized Benjamin equation \begin{equation}\label{Benj-IVP} \begin{cases} \partial_t u-l\mathcal{H} \partial_x^2u-\partial_x^3u+u^p\partial_xu = 0, \quad x,\; t\in \mathbb{R};\;\;,\; p\geq 1, \\ u(x,0) = u_0(x), \end{cases} \end{equation} where $u=u(x,t)$ is a real valued function, $0

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete and Continuous Dynamical Systems 数学-数学

CiteScore

2.50

自引率

0.00%

发文量

175

审稿时长

6 months

期刊介绍： DCDS, series A includes peer-reviewed original papers and invited expository papers on the theory and methods of analysis, differential equations and dynamical systems. This journal is committed to recording important new results in its field and maintains the highest standards of innovation and quality. To be published in this journal, an original paper must be correct, new, nontrivial and of interest to a substantial number of readers.