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Solvability of a nonlocal problem for an evolution equation with a superstable semigroupстатья
Информация о цитировании статьи получена из
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Дата последнего поиска статьи во внешних источниках: 4 ноября 2020 г.
- Авторы: Tikhonov I.V., Vu Nguyen Son Tung
- Журнал: Differential Equations
- Том: 56
- Номер: 4
- Год издания: 2020
- Издательство: Pleiades Publishing, Inc.
- Местоположение издательства: New York, USA
- Первая страница: 478
- Последняя страница: 498
- DOI: 10.1134/S0012266120040072
- Аннотация: We study a linear nonlocal problem for an evolution equation in a Banach space. The standard semigroup approach is used but integral averaging over time is used instead of the traditional initial condition. It is assumed that the evolution semigroup associated with the abstract differential equation is superstable (quasinilpotent), i.e., has an infinite negative exponential type. A theorem about unique solvability of the posed nonlocal problem is proved. It is shown that the solution can be represented by a convergent Neumann series. Some corollaries are noted. The case in which the semigroup is nilpotent is treated separately. The class of examples of superstable semigroups that are of interest in mathematical physics is outlined.
- Добавил в систему: Ву Нгуен Шон Тунг Тунг