|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ПсковГУ |
||
On a criterion for the solvability of one ill-posed problem for the biharmonic equationстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 9 марта 2017 г.
- Авторы: Kal'menov Tynysbek S., Sadybekov Makhmud A., Iskakova Ulzada A.
- Журнал: Journal of Inverse and Ill-Posed Problems
- Том: 24
- Номер: 6
- Год издания: 2016
- Издательство: V S P
- Местоположение издательства: Netherlands
- Первая страница: 777
- Последняя страница: 783
- DOI: 10.1515/jiip-2016-0003
- Аннотация: A local boundary value problem for an inhomogeneous biharmonic equation in a rectangular domain is considered. Boundary conditions are given on the whole boundary of the domain. It is shown that the problem turns out to be self-adjoint. And herewith the problem is ill-posed. An example is constructed demonstrating that the solution stability to the problem is violated. Necessary and sufficient conditions of the existence of a strong solution to the investigated problem are found. The idea of the method is that the solution to the problem is constructed in the form of an expansion on eigenfunctions of this self-adjoint problem. This problem has an isolated point of continuous spectrum in zero. It is shown that there exists a series (a sequence) of eigenvalues converging to zero. Asymptotics of these eigenvalues is found. Namely this asymptotics defines a reason for the ill-posedness of the investigated problem. A space of well-posedness for the investigated problem is constructed.
- Добавил в систему: Садыбеков Махмуд Абдысаметович