# Problem Formulation

Below is the mathematical formulation of the
control problem.
The function *y* denotes the temperature
of the probe and *u* is the control.
The point *x=1* represents the inside of
the probe and *x=0* the outside.
The function *yd* represents the desired
temperature distribution inside the probe.
The functions *T* (tau) and
*k* (kappa) denote the specific heat capacity and
the heat conduction, respectively,
*y0* is the initial temperature distribution,
*q* is the source term, and *g* is a given scalar.