On One Control Problem for Zakharov–Kuznetsov Equation

An initial-boundary value problem for Zakharov–Kuznetsov equation u t + bu x + u xxx + u xyy + uu x = f 0 (t)g(t, x, y) posed on a rectangle (0, R) × (0, L) for t ∈ (0, T) under certain initial and boundary conditions is considered. Here, the function f 0 is unknown and is referred as a control, and the function g is given. The problem is to find a pair (f 0 , u), satisfying the additional condition ∫0Tu(t,x,y)ω(x,y)dxdy=φ(t), where the functions ω, φ are given and u is the solution to the corresponding initial-boundary value problem. It is shown that under certain smallness assumptions on input data such a pair exists and is unique. For the corresponding linearized equation, a similar result is obtained without any smallness assumptions. © Springer Nature Switzerland AG 2019.

Авторы
Редакторы
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Сборник статей
Издательство
Springer International Publishing
Номер выпуска
-
Язык
Английский
Страницы
305-313
Статус
Опубликовано
Подразделение
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Ссылка
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Номер
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Том
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Год
2019
Организации
  • 1 RUDN University, Moscow, Russian Federation
Ключевые слова
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Дата создания
19.07.2019
Дата изменения
19.07.2019
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/38950/