Pub Date : 2017-11-06DOI: 10.4208/csiam-am.2020-0001
K. Ammari, M. Choulli, Faouzi Triki
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.
{"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":"https://doi.org/10.4208/csiam-am.2020-0001","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":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41497643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-06-05DOI: 10.4208/csiam-am.2020-0017
Li Chen, Ruo Li, Feng Yang
We proposed a piecewise quadratic reconstruction method, which is in an integrated style, for finite volume schemes to scalar conservation laws. This quadratic reconstruction is parameter-free, is of third-order accuracy for smooth functions, and is flexible on structured and unstructured grids. The finite volume schemes with the new reconstruction satisfy a local maximum principle. Numerical examples are presented to show that the proposed schemes with a third-order Runge-Kutta method attain the expected order of accuracy.
{"title":"An Integrated Quadratic Reconstruction for Finite Volume Schemes to Scalar Conservation Laws in Multiple Dimensions","authors":"Li Chen, Ruo Li, Feng Yang","doi":"10.4208/csiam-am.2020-0017","DOIUrl":"https://doi.org/10.4208/csiam-am.2020-0017","url":null,"abstract":"We proposed a piecewise quadratic reconstruction method, which is in an integrated style, for finite volume schemes to scalar conservation laws. This quadratic reconstruction is parameter-free, is of third-order accuracy for smooth functions, and is flexible on structured and unstructured grids. The finite volume schemes with the new reconstruction satisfy a local maximum principle. Numerical examples are presented to show that the proposed schemes with a third-order Runge-Kutta method attain the expected order of accuracy.","PeriodicalId":29749,"journal":{"name":"CSIAM Transactions on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2017-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45029808","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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