CARLEMAN ESTIMATE FOR LINEAR VISCOELASTICITY EQUATIONS AND AN INVERSE SOURCE PROBLEM

We consider the linear system of viscoelasticity with the homogeneous Dirichlet boundary condition. First we prove a Carleman estimate with boundary values of solutions of the viscoelasticity system. Since a solution u under consideration is not assumed to have compact support, in the decoupling of the Lame operator by introducing the divergence and the n-dimensional rotation of u, we have no boundary condition for them, so that we have to carry out arguments by a pseudodifferential operator. Second we apply the Carleman estimate to an inverse source problem of determining a spatially varying factor of the external source in the linear viscoelastitiy by extra Neumann data on a suitable lateral subboundary over a sufficiently long time interval and establish a stability estimate.

Авторы
Imanuvilov O.Y.1 , Yamamoto M. 2, 3, 4
Редакторы
-
Издательство
-
Номер выпуска
1
Язык
Английский
Страницы
718-791
Статус
Опубликовано
Подразделение
-
Ссылка
-
Номер
-
Том
52
Год
2020
Организации
  • 1 Colorado State Univ, Dept Math, 101 Weber Bldg, Ft Collins, CO 80523 USA
  • 2 Univ Tokyo, Dept Math Sci, Meguro Ku, Tokyo 1538914, Japan
  • 3 Acad Romanian Scientists, Splaiul Independentei St 54, Bucharest 050094, Romania
  • 4 RUDN Univ, Peoples Friendship Univ Russia, 6 Miklukho Maklaya St, Moscow 117198, Russia
Ключевые слова
Carleman estimate; inverse problem; linear viscoelasticity
Дата создания
02.11.2020
Дата изменения
02.11.2020
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/66051/