Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Point-Wise Control
DOI:
https://doi.org/10.15407/mag18.01.075Анотація
У роботі вивчено проблеми керованості та наближеної керованості для керованої системи $w_t=\Delta w$, $w(0,x_2,t)=u(t)\delta(x_2)$, $x_1>0$, $x_2\in\mathbb R$, $t\in(0,T)$, де $u\in L^\infty(0,T)$ є керуванням. У термінах розв'язності степеневої проблеми моментів Маркова одержано необхідні і достатні умови керованості та достатні умови наближеної керованості за заданий час $T$, коли керування $u$ є обмеженим заданою сталою. Побудовано ортогональні базиси в спеціальних просторах соболєвського типу. Застосовуючи ці базиси, одержано необхідні і достатні умови наближеної керованості і чисельне розв'язання проблеми наближеної керованості. Результати проілюстровано прикладом.Mathematics Subject Classification: 93B05, 35K05, 35B30
Ключові слова:
рівняння теплопровідності, керованість, наближена керованість, точкове керування, півплощинаПосилання
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