Theoretical stability in coefficient inverse problems for general hyperbolic equations with numerical reconstruction

In this article, we investigate the determination of the spatial component in the time-dependent second order coefficient of a hyperbolic equation from both theoretical and numerical aspects. By the Carleman estimates for general hyperbolic operators and an auxiliary Carleman estimate, we establish local Hölder stability with either partial boundary or interior measurements under certain geometrical conditions. For numerical reconstruction, we minimize a Tikhonov functional which penalizes the gradient of the unknown function. Based on the resulting variational equation, we design an iteration method which is updated by solving a Poisson equation at each step. One-dimensional prototype examples illustrate the numerical performance of the proposed iteration. © 2018 IOP Publishing Ltd.

Авторы
Yu J.1 , Liu Y.2 , Yamamoto M. 2, 3
Редакторы
-
Журнал
Издательство
Institute of Physics Publishing
Номер выпуска
4
Язык
Английский
Страницы
-
Статус
Опубликовано
Подразделение
-
Номер
045001
Том
34
Год
2018
Организации
  • 1 School of Mathematical Sciences, Fudan University, No. 220 Handan Road, Shanghai, 200433, China
  • 2 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • 3 Research Center of Nonlinear Problems of Mathematical Physics, Peoples' Friendship University of Russia, 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation
Ключевые слова
Carleman estimate; coefficient inverse problem; hyperbolic equation; iteration method; local Holder stability
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/6837/