Разрешимость модельной нелокальной задачи для общего уравнения переноса нейтронов

Автор: Ву Нгуен Шон Тунг
Журнал: Вестник Воронежского государственного университета. Серия: Физика. Математика
Номер: 1
Год издания: 2018
Первая страница: 69
Последняя страница: 81
Аннотация: SOLVABILITY OF THE MODEL NONLOCAL PROBLEM ASSOCIATED WITH THE GENERAL NEUTRON. A special nonlocal problem for the general nonstationary neutron transport equation is studied. The transport equation is interpreted as an evolutionary equation in the Banach space of summable functions. Instead of the traditional initial condition, an integral expressing the time averages is given. The main results are obtained on the basis of a general theory developed for an abstract nonlocal problem in a Banach space. Under natural restrictions the existence and uniqueness theorem for a weak solution is established. An estimate of the stability is found, and it is shown that a weak solution can be represented by a convergent Neumann series. Precise conditions are noted, under which the weak solution is a classical solution. In the case when the transport equation is taken without the collision integral, we show that the solution could be found explicitly, in the form of a finite sum. In the study of the problem, the theory of semigroups of bounded linear operators in a Banach space is used.
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