Controllability problems for the heat equation with variable coefficients on a half-axis

In the paper, the problems of controllability and approximate controllability are studied for the heat equation wt = 1/ρ (kwx)x + γw, x > 0, t ∈ (0, T), controlled by the Dirichlet boundary condition. Control is considered in L∞(0, T). It is proved that each initial state of this system is approximately controllable to any its end state in a given time T > 0.