{"title":"一类变阶分数阶波动方程的局部修正与分析","authors":"Shuyu Li , Hong Wang , Jinhong Jia","doi":"10.1016/j.aml.2024.109425","DOIUrl":null,"url":null,"abstract":"<div><div>We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>, we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"163 ","pages":"Article 109425"},"PeriodicalIF":2.9000,"publicationDate":"2024-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local modification and analysis of a variable-order fractional wave equation\",\"authors\":\"Shuyu Li , Hong Wang , Jinhong Jia\",\"doi\":\"10.1016/j.aml.2024.109425\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at <span><math><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math></span>, we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"163 \",\"pages\":\"Article 109425\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965924004452\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924004452","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Local modification and analysis of a variable-order fractional wave equation
We investigate a local modification of a variable-order time-fractional wave equation, which models the vibrations of a viscoelastic bar along its longitudinal axis. Under suitable assumptions regarding the variable order at , we prove that the original model is equivalent to a multiscale wave equation. Furthermore, we analyze the well-posedness of its weak solution. Numerical experiments are implemented to clarify the theoretical analysis.
期刊介绍：
The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.
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