六阶布辛斯方程的良好求解和解析性

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2024-02-16 DOI:10.1142/s0219199724500056

Amin Esfahani, Achenef Tesfahun

{"title":"六阶布辛斯方程的良好求解和解析性","authors":"Amin Esfahani, Achenef Tesfahun","doi":"10.1142/s0219199724500056","DOIUrl":null,"url":null,"abstract":"In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term <math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi mathvariant=\"normal\">Δ</mi><mi>u</mi></math> in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.","PeriodicalId":50660,"journal":{"name":"Communications in Contemporary Mathematics","volume":"88 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation\",\"authors\":\"Amin Esfahani, Achenef Tesfahun\",\"doi\":\"10.1142/s0219199724500056\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term <math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi mathvariant=\\\"normal\\\">Δ</mi><mi>u</mi></math> in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.\",\"PeriodicalId\":50660,\"journal\":{\"name\":\"Communications in Contemporary Mathematics\",\"volume\":\"88 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Contemporary Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/s0219199724500056\",\"RegionNum\":2,\"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":"Communications in Contemporary Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219199724500056","RegionNum":2,"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

本文研究了六阶布辛斯方程。我们将该方程的二次方和三次方非线性的局部好求解理论扩展到高维情况。尽管方程中存在 "坏 "的第四项 Δu，我们仍推导出了一些分散估计值，从而得出了局部解的存在性，这也改进了之前三次方程的结果。此外，我们还展示了立方非线性解的空间解析性的持久性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation

In this paper, the sixth-order Boussinesq equation is studied. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the “bad” fourth term $Δ u$ in the equation, we derive some dispersive estimates leading to the existence of local solutions which also improves the previous results in the cubic case. In addition, we show persistence of spatial analyticity of solutions for the cubic nonlinearity.

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

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.