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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Modified Sobolev Spaces in Controllability Problems for the Wave Equation on a Half-Plane
L. V. Fardigola B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkiv 61103, Ukraine
Аннотация:
The $2$-d wave equation $w_{tt}=\Delta w$, $t\in(0,T)$, on the half-plane $x_1>0$ controlled by the Neumann boundary condition $w_{x_1}(0,x_2,t)=\delta(x_2)u(t)$ is considered in Sobolev spaces, where $T>0$ is a constant and $u\in L^\infty(0,T)$ is a control. This control system is transformed into a control system for the $1$-d wave equation in modified Sobolev spaces introduced and studied in the paper, and they play the main role in the study. The necessary and sufficient conditions of (approximate) $L^\infty$-controllability are obtained for the $1$-d control problem. It is also proved that the $2$-d control system replicates the controllability properties of the $1$-d control system and vise versa. Finally, the necessary and sufficient conditions of (approximate) $L^\infty$-controllability are obtained for the $2$-d control problem.
Ключевые слова и фразы:
modified Sobolev space, wave equation, half-plane, controllability problem, Neumann boundary control.
Поступила в редакцию: 26.11.2013 Исправленный вариант: 15.10.2014
Образец цитирования:
L. V. Fardigola, “Modified Sobolev Spaces in Controllability Problems for the Wave Equation on a Half-Plane”, Журн. матем. физ., анал., геом., 11:1 (2015), 18–44
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag608 https://www.mathnet.ru/rus/jmag/v11/i1/p18
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Страница аннотации: | 218 | PDF полного текста: | 46 | Список литературы: | 30 |
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