Controllability Problems for the Heat Equation with Variable Coefficients on a Half-Axis Controlled by the Neumann Boundary Condition

In the paper, the problems of controllability and approximate controllability are studied for the control systemIt is proved that any initial state of the control system is not controllable to the origin except the zero initial state in a given time T > 0. However, each initial state of the control system is approximately controllable to any target state in a given time T > 0. Due to transformation operator generated by the equation data ρ, k, γ, the main results are obtained from their analogues obtained earlier in the case of constant coefficients (ρ = k = 1, γ = 0).Applying this operator is a focal point of the paper.The results are illustrated by examples.