|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ИНХС РАН |
||
Inverse Problem with Overdetermination of the Third Kind for an Abstract Second-Order Differential Equationстатья
- Авторы: Tikhonov I.V., Almohamed M.
- Журнал: Differential Equations
- Том: 58
- Номер: 7
- Год издания: 2022
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 877
- Последняя страница: 898
- DOI: 10.1134/S0012266122070035
- Аннотация: We consider a linear inverse problem for an abstract second-order differential equation in a Banach space. The time-invariant inhomogeneous term in the equation is assumed to be unknown. The standart Cauchy conditions are set at the initial time. They are supplemented with an additional condition, a final overdetermination of the third kind, which contains a combination of values of the evolution function and its derivative at a select final time. A criterion for the uniqueness of the solution expressed in spectral terms via the zeros of characteristic entire function is established for the problem. The result is universal and does not reqire any restrictions on the type of the differential equation. The distribution of zeros of the characteristic function is discussed separately. Our analysis gives a number of efficient sufficient test for the uniqueness (and nonuniqueness) of the solution. All of these test are simple and convenient in practice.
- Добавил в систему: Тихонов Иван Владимирович