{"title":"浅水波方程爆炸的充分条件","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":"{\"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}","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
摘要
研究了 R 线上浅水波方程的炸波特征。利用 L2 守恒定律推导出方程解的若干估计值。建立了解的破浪和寿命的充分条件。我们的主要结果包含了之前文献中 Fornberg-Whitham 和 Degasperis-Procesi 方程的部分破浪条件。
Sufficient conditions of blowup to a shallow water wave equation
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
