{"title":"（综述文章）利用可观察性不等式求解发展方程某些逆问题的统一方法","authors":"K. Ammari, M. Choulli, Faouzi Triki","doi":"10.4208/csiam-am.2020-0001","DOIUrl":null,"url":null,"abstract":"We survey some of our recent results on inverse problems for evolution equations. The goal is to provide an unified approach to solve various type of evolution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on observability inequalities, and a special choice of initial conditions we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"(REVIEW ARTICLE) A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities\",\"authors\":\"K. Ammari, M. Choulli, Faouzi Triki\",\"doi\":\"10.4208/csiam-am.2020-0001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We survey some of our recent results on inverse problems for evolution equations. The goal is to provide an unified approach to solve various type of evolution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on observability inequalities, and a special choice of initial conditions we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.\",\"PeriodicalId\":29749,\"journal\":{\"name\":\"CSIAM Transactions on Applied Mathematics\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2017-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"CSIAM Transactions on Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4208/csiam-am.2020-0001\",\"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":"CSIAM Transactions on Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4208/csiam-am.2020-0001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
(REVIEW ARTICLE) A Unified Approach to Solving Some Inverse Problems for Evolution Equations by Using Observability Inequalities
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide an unified approach to solve various type of evolution equations. The inverse problems we consider consist in determining unknown coefficients from boundary measurements by varying initial conditions. Based on observability inequalities, and a special choice of initial conditions we provide uniqueness and stability estimates for the recovery of volume and boundary lower order coefficients in wave and heat equations. Some of the results presented here are slightly improved from their original versions.
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