Boundedness and stability of temperature in thermistors

The evolution of temperature along thermistors can be modeled by a reaction-diffusion equation. In this paper, it is proved that the mathematical model of temperature evolution in thermistors has a unique, bounded, and non-negative solution. It is further proved that the steady-state temperature profile of thermistors is unique and asymptotically stable. Finally, the bounded-input bounded-output (BIBO) stability of a class of systems represented by nonlinear partial differential equations of reaction-diffusion type, to which the thermistor model belongs, is established.