Stability analysis of explosive crystallization front in the ESPE mode

We consider a nonlinear two-dimensional heat conduction model for the dynamics of explosive crystallization (in the ESPE mode) of amorphous films in the case when some thermophysical properties of the amorphous and crystalline phases differ. Conditions for the linear monotonic and oscillatory instabilities of a plane crystallization front are found. For the description of the nonlinear development of the instability, nonlocally coupled complex Ginzburg-Landau equations for the amplitudes of the unstable modes, which involve averaged terms, are derived. The plane wave solutions of the amplitude equations are found, and the regions of stability for these solutions are determined.