{"title":"Improved Lower Bound for the Radius of Analyticity of Solutions to the Fifth Order, KdV-BBM Type Equation","authors":"Sileshi Mebrate, Tamirat Dufera, Achenef Tesfahun","doi":"10.1007/s41980-024-00882-z","DOIUrl":null,"url":null,"abstract":"<p>We show that the uniform radius of spatial analyticity <span>\\(\\sigma (t)\\)</span> of solutions at time <i>t</i> to the fifth order, KdV-BBM type equation cannot decay faster than <span>\\(1/ \\sqrt{t}\\)</span> for large <i>t</i>, given initial data that is analytic with fixed radius <span>\\(\\sigma _0\\)</span>. This improves a recent result by Belayneh, Tegegn and the third author [2], where they obtained a 1/<i>t</i> decay of <span>\\(\\sigma (t)\\)</span> for large time <i>t</i>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-024-00882-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that the uniform radius of spatial analyticity \(\sigma (t)\) of solutions at time t to the fifth order, KdV-BBM type equation cannot decay faster than \(1/ \sqrt{t}\) for large t, given initial data that is analytic with fixed radius \(\sigma _0\). This improves a recent result by Belayneh, Tegegn and the third author [2], where they obtained a 1/t decay of \(\sigma (t)\) for large time t.
期刊介绍：
The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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