Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition
DOI:
https://doi.org/10.15407/mag19.03.616Анотація
У роботi дослiджено проблеми керованостi та наближеної керованостi для керованої системи $w_t=\frac{1}{\rho}\left(kw_x\right)_x+\gamma w$, $\left.\left(\sqrt{\frac{k}{\rho}}w_x\right)\right|_{x=0}=u$, $x>0$, $t\in(0,T)$, де $u$ є керуванням, $u\in L^\infty(0,T)$. Доведено, що жодний початковий стан (крiм нульового) не може бути скерованим до нуля за заданий час $T>0$. Проте, кожний початковий стан керованої системи є наближено керованим у будь-який цiльовий стан за заданий час $T>0$. Завдяки оператору перетворення, породженому параметрами рiвняння $\rho$, $k$, $\gamma$, основнi результати роботи одержано з їх аналогiв для випадку сталих коефiцiєнтiв ($\rho=k=1$, $\gamma=0$). Застосування цього оператора є ключовим моментом роботи. Результати проiлюстровано прикладами.
Mathematical Subject Classification 2020: 93B05, 35K05, 35B30.
Ключові слова:
рiвняння теплопровiдностi, керованiсть, наближена керованiстьПосилання
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