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

摘要

In the paper, problems of controllability, approximate controllability,reachability and approximate reachability are studied for the control systemwt = wxx, 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 ina given time T, and each its initial state is approximately controllable in agiven time T. A necessary and sufficient condition for reachability in a giventime 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 agiven time T. The results are illustrated by examples.