{"title":"On conservative solutions to the generalized hyperelastic-rod equation","authors":"Yu Gao","doi":"10.1016/j.jde.2025.113355","DOIUrl":null,"url":null,"abstract":"<div><div>This paper investigates a generalized hyperelastic-rod wave equation within its generalized framework. For conservative solutions, we establish that the singularities of the energy measure can only occur at countably many times. Furthermore, we prove the uniqueness of the solution by employing a refined characteristics method.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"438 ","pages":"Article 113355"},"PeriodicalIF":2.3000,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039625003821","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/4/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates a generalized hyperelastic-rod wave equation within its generalized framework. For conservative solutions, we establish that the singularities of the energy measure can only occur at countably many times. Furthermore, we prove the uniqueness of the solution by employing a refined characteristics method.
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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