Control of the temperature at one end of a rod

We present some graphical output from numerical studies of the control of the temperature at one end (x = 0) of a rod by changing the heat flux at the other end (x = b). The changes in the heat flux at b are initiated by a thermostat at 0. Because a thermostat is a device with hysteresis, the theoretical analysis of such problems can be challenging. The studies we present show some of the important features to be examined in theoretical work.