Optimal boundary control of heat transfer in a three-dimensional material: A hyperbolic model

We consider a boundary value problem that describes heat propagation in a homogeneous isotropic body in the framework of the hyperbolic heat conduction model. We construct a class of boundary data (controls) depending on a functional parameter and providing a given distribution of the body temperature at a given time. By using the Lagrange method, from the constructed class, we choose a subclass of controls minimizing a given loss function.