{"title":"Sufficient conditions of blowup to a shallow water wave equation","authors":"Changtai Zhou , Jin Hong , Shaoyong Lai","doi":"10.1016/j.rinam.2024.100487","DOIUrl":null,"url":null,"abstract":"<div><p>The blow-up features of a shallow water wave equation on the line <span><math><mi>R</mi></math></span> are investigated. The <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> conservation law is utilized to derive several estimates of solutions for the equation. Sufficient conditions for wave breaking and lifespan of the solutions are established. Our main results contain parts of the wave breaking conditions for the Fornberg–Whitham and Degasperis–Procesi equations in the previous literatures.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100487"},"PeriodicalIF":1.4000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000578/pdfft?md5=2ec6900f6f3d97ef55eb86cf1702e048&pid=1-s2.0-S2590037424000578-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037424000578","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The blow-up features of a shallow water wave equation on the line are investigated. The conservation law is utilized to derive several estimates of solutions for the equation. Sufficient conditions for wave breaking and lifespan of the solutions are established. Our main results contain parts of the wave breaking conditions for the Fornberg–Whitham and Degasperis–Procesi equations in the previous literatures.
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