Evolution of the radius of analyticity for the generalized Benjamin equation

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":"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}
引用次数: 0

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, $0
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
广义本雅明方程解析半径的演化
本文研究广义本杰明方程\begin{equation}\label{Benj-IVP} \begin{cases} \partial_t u-l\mathcal{H} \partial_x^2u-\partial_x^3u+u^p\partial_xu = 0, \quad x,\; t\in \mathbb{R};\;\;,\; p\geq 1, \\ u(x,0) = u_0(x), \end{cases} \end{equation}的初值问题,其中$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。
求助全文
约1分钟内获得全文 去求助
来源期刊
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.
期刊最新文献
On a structure of non-wandering set of an $ \Omega $-stable 3-diffeomorphism possessing a hyperbolic attractor Existence analysis for a reaction-diffusion Cahn–Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth Propagation dynamics of a nonlocal reaction-diffusion system Global boundedness of a three-species predator-prey model with prey-taxis and competition Robust non-hyperbolic fibred quadratic polynomial dynamics
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1