Below is the mathematical formulation of the
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.