Reachability and Controllability Problems for the Heat Equation on a Half-Axis

Analysis, Geometry Reachability and Controllability Problems for the Heat Equation on a Half-Axis Larissa Fardigola and Kateryna KhalinaIn the paper, problems of controllability, approximate controllability, reachability and approximate reachability are studied for the control system w t = w xx , w(0, •) = u, x > 0, t ∈ (0, T ), where u ∈ L ∞ (0, T ) is a control.It is proved that each end state of this system is approximately reachable in a given time T , and each its initial state is approximately controllable in a given time T .A necessary and sufficient condition for reachability in a given time T is obtained in terms of solvability a Markov power moment problem.It is also shown that there is no initial state that is null-controllable in a given time T .The results are illustrated by examples.