Front propagation in a phase field model with phase-dependent heat absorption

In cases where the heat absorption of the crystal phase is less than that in the amorphous state, we find that there is a bi-stability of the phases. We investigate the spatial behaviours that are a consequence of this property and use a phase field model for the spatio-temporal dynamics in which the phase variable is coupled to a suitable temperature field. It is shown that travelling wave solutions of the system exist and, depending on the precise system parameters, these waves can take a range of forms and velocities. Some examples of possible dynamical behaviours are discussed and, in particular, we demonstrate that the waves may collide and annihilate. The longitudinal and transverse stability of the travelling waves are examined using an Evans function method which suggests that the fronts are stable structures.