Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb{R}_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a special subset of $L^\infty(\mathbb{R}\times (0,T))\cap L^2(\mat...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2026
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| Online Zugang: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1125 |
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| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Zusammenfassung: | In the paper, the problems of approximate controllability are studied for the control system $w_t=\Delta w$, $w(0,x_2,t)=u(x_2,t)$, $x_1\in\mathbb{R}_+=(0,+\infty)$, $x_2\in\mathbb R$, $t\in(0,T)$, where $u$ is a control belonging to a special subset of $L^\infty(\mathbb{R}\times (0,T))\cap L^2(\mathbb{R}\times (0,T))$. It is proved that each initial state belonging to $L^2(\mathbb{R}_+\times\mathbb{R})$ is approximately controllable to an arbitrary end state belonging to $L^2(\mathbb{R}_+\times\mathbb{R})$ by applying these controls. A numerical algorithm of solving the approximate controllability problem for this system is given. The results are illustrated by an example.
Mathematical Subject Classification 2020: 93B05, 35K05, 35B30 |
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