Inverse Problems for a Compressible Fluid System

In this article, we discuss the methodology based on Carleman estimates concerning the unique continuation and inverse problems of determining spatially varying coefficients. First as retrospective views we refer to main works by that methodology starting from the pioneering work by Bukhgeim and Klibanov published in 1981. Then as one possible object of the application of this methodology, we start to consider compressible fluid flows and we prove conditional stability estimates for an inverse source problem and the continuation of solutions from a part of lateral boundary. We apply two types of Carleman estimates respectively with a weight function which is quadratic in time and a weight function which rapidly decays at the end points of the time interval. © 2020, Springer Nature Singapore Pte Ltd.

Авторы
Imanuvilov O.Y.1 , Yamamoto M. 2, 3, 4
Сборник материалов конференции
Издательство
Springer New York LLC
Язык
Английский
Страницы
101-148
Статус
Опубликовано
Том
310
Год
2020
Организации
  • 1 Department of Mathematics, Colorado State University, 101 Weber Building, Fort Collins, CO 80523-1874, United States
  • 2 Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan
  • 3 Honorary Member of Academy of Romanian Scientists, Splaiul Independentei Street, No. 54, Bucharest, 050094, Romania
  • 4 Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation
Ключевые слова
Carleman estimate; Compressible viscous fluid; Conditional stability; Inverse source problem; Unique continuation
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/65544/