Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition

Автор(и)

  • Larissa Fardigola B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
    V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine
  • Kateryna Khalina B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine

DOI:

https://doi.org/10.15407/mag19.03.616

Анотація

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 керованiсть

Посилання

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Fardigola, L.; Khalina, K. Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition. Журн. мат. фіз. анал. геом. 2023, 19, 616-641.

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