Approximate Controllability Problems for the Heat Equation in a Half-Plane Controlled by the Dirichlet Boundary Condition with a Bounded Control
Abstract
In the paper, the problems of approximate controllability are studied for the control system w t = ∆w, w(0, x 2 , t) = u(x 2 , t), x 1 ∈ R + = (0, +∞), x 2 ∈ R, t ∈ (0, T ), where u is a control belonging to a special subset of L ∞ (R × (0, T )) ∩ L 2 (R × (0, T )).It is proved that each initial state belonging to L 2 (R + ×R) is approximately controllable to an arbitrary end state belonging to L 2 (R + × 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.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Differential Equations and Boundary Problems
Nonlinear Differential Equations Analysis
Publication details
- Journal / source
- Zurnal matematiceskoj fiziki analiza geometrii
- Volume
- 22
- Issue
- 1
- Pages
- 34–65
- Publication date
- 25 January 2026
- Language
- EN