{"title":"多期时间分式波方程的阶次和势的唯一反演","authors":"Xuyan Jiang, Zhiyuan Li","doi":"10.1016/j.aml.2024.109319","DOIUrl":null,"url":null,"abstract":"<div><div>The paper investigates an inverse problem of determining the orders and potential function of multi-term time fractional wave equations. By analyzing the asymptotic behavior of the multivariate Mittag–Leffler function, we show the uniqueness of the inverting the orders and potential term using interior domain measurement data. The article also provides numerical simulations, showing how to handle noisy data and reconstruct the parameters of the equation through Tikhonov regularization.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109319"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unique inversion of orders and potential for multi-term time fractional wave equations\",\"authors\":\"Xuyan Jiang, Zhiyuan Li\",\"doi\":\"10.1016/j.aml.2024.109319\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>The paper investigates an inverse problem of determining the orders and potential function of multi-term time fractional wave equations. By analyzing the asymptotic behavior of the multivariate Mittag–Leffler function, we show the uniqueness of the inverting the orders and potential term using interior domain measurement data. The article also provides numerical simulations, showing how to handle noisy data and reconstruct the parameters of the equation through Tikhonov regularization.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"160 \",\"pages\":\"Article 109319\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-09-28\",\"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/S0893965924003392\",\"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/S0893965924003392","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Unique inversion of orders and potential for multi-term time fractional wave equations
The paper investigates an inverse problem of determining the orders and potential function of multi-term time fractional wave equations. By analyzing the asymptotic behavior of the multivariate Mittag–Leffler function, we show the uniqueness of the inverting the orders and potential term using interior domain measurement data. The article also provides numerical simulations, showing how to handle noisy data and reconstruct the parameters of the equation through Tikhonov regularization.
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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