The Reflection Principle in the Control Problem of the Heat Equation

We consider the control problem for generalized heat equation a Schroedinger operator on domain with reflection symmetry respect to hyperplane. show that if this system is null-controllable, then so its respective parts and corresponding cost does not exceed one whole domain. As an application, we obtain null-controllability results half-spaces, orthants, sectors of angle $\pi/2$. byproduct, also explicit bounds certain triangles prisms in terms geometric parameters set.