Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
Анотація
У роботі досліджено проблеми наближеної керованості для керованої системи $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb{R}_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, де $u$ є керуванням, що належить до деякої спеціальної підмножини $L^\infty(\mathbb{R}\times (0,T))\cap L^2(\mathbb{R}\times (0,T))$. Доведено, що кожен початковий стан, що належить $L^2(\mathbb{R}_+\times\mathbb{R})$, є наближено керованим за допомогою таких керувань у будь-який кінцевий стан, що належить $L^2(\mathbb{R}_+\times\mathbb{R})$. Побудовано числовий алгоритм розв'язання проблеми наближеної керованості для цієї системи. Результати проілюстровано прикладом.
Mathematical Subject Classification 2020: 93B05, 35K05, 35B30
Ключові слова:
рівняння теплопровідності, керованість, наближена керованість, півплощинаПосилання
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