Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data. © 2017 IOP Publishing Ltd.

Авторы
Beilina L.1 , Cristofol M.2 , Li S.3 , Yamamoto M. 4, 5
Редакторы
-
Журнал
Издательство
Institute of Physics Publishing
Номер выпуска
1
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
015001
Том
34
Год
2018
Организации
  • 1 Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Gothenburg, SE-42196, Sweden
  • 2 Institut de Mathématiques de Marseille, CNRS, UMR 7373, École Centrale, Aix-Marseille Université, Marseille, 13453, France
  • 3 Key Laboratory of Wu Wen-Tsun Mathematics, USTC, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science, Technology of China, 96 Jinzhai Road, Anhui Province, Hefei, 230026, China
  • 4 Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153, Japan
  • 5 Research Center Center of Nonlinear Problems of Mathematical Physics, Peoples' Friendship University of Russia, 6 Miklucho-Maklaya, Moscow, 117198, Russian Federation
Ключевые слова
adaptive algorithm; an acoustic equation of hyperbolic type; Carleman estimate; coefficient inverse problem; two space-dependent coefficients
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/7405/