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...
Збережено в:
| Дата: | 2026 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2026
|
| Теми: | |
| Онлайн доступ: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1125 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Journal of Mathematical Physics, Analysis, Geometry |
Репозитарії
Journal of Mathematical Physics, Analysis, Geometry| _version_ | 1859471873704722432 |
|---|---|
| author | Fardigola, Larissa Khalina, Kateryna |
| author_facet | Fardigola, Larissa Khalina, Kateryna |
| author_sort | Fardigola, Larissa |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2026-02-21T09:54:07Z |
| description | 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 |
| first_indexed | 2026-03-12T15:49:27Z |
| format | Article |
| id | oai:jmag.ilt.kharkiv.ua:article-1125 |
| institution | Journal of Mathematical Physics, Analysis, Geometry |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-12T15:49:27Z |
| publishDate | 2026 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України |
| record_format | ojs |
| spelling | oai:jmag.ilt.kharkiv.ua:article-11252026-02-21T09:54:07Z Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control Fardigola, Larissa Khalina, Kateryna рівняння теплопровідності керованість наближена керованість півплощина heat equation controllability approximate controllability half-plane 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 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 Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2026-02-20 Article Article application/pdf https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1125 10.15407/mag22.01.03 Journal of Mathematical Physics, Analysis, Geometry; Vol. 22 No. 1 (2026); 34–65 Журнал математической физики, анализа, геометрии; Том 22 № 1 (2026); 34–65 Журнал математичної фізики, аналізу, геометрії; Том 22 № 1 (2026); 34–65 1817-5805 1812-9471 en https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1125/jm22-0034e |
| spellingShingle | рівняння теплопровідності керованість наближена керованість півплощина Fardigola, Larissa Khalina, Kateryna Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_alt | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_full | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_fullStr | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_full_unstemmed | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_short | Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control |
| title_sort | approximate controllability problems for the heat equation in a half-plane controlled by the dirichlet boundary condition with a bounded control |
| topic | рівняння теплопровідності керованість наближена керованість півплощина |
| topic_facet | рівняння теплопровідності керованість наближена керованість півплощина heat equation controllability approximate controllability half-plane |
| url | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1125 |
| work_keys_str_mv | AT fardigolalarissa approximatecontrollabilityproblemsfortheheatequationinahalfplanecontrolledbythedirichletboundaryconditionwithaboundedcontrol AT khalinakateryna approximatecontrollabilityproblemsfortheheatequationinahalfplanecontrolledbythedirichletboundaryconditionwithaboundedcontrol |