Dynamic transitions for Landau-Brazovskii model (Q2438868)

The technical approach of the dynamic phase transition theory was first developed by \textit{T. Ma} and \textit{S. Wang} [Phase transition dynamics. New York, NY: Springer (2014; Zbl 1285.82004)]. The main philosophy of this theory is to search for the full set of transition states, giving a complete characterization of stability and transition. The dynamic transition theory consists in identifying the transition states and classifying them both dynamically and physically. One important ingredient of this theory is the introduction of a dynamic classification scheme of phase transitions. Using this approach, the authors study the disordered and ordered phase transition modelled by the Landau-Brazovskii (LB) equation (Ginzburg-Landau type equation) \[ \varphi_t=\frac{D\xi_0^2}{4q^2_0}\Delta (\Delta+q^2_0)^2\varphi+\tau D\Delta \varphi-\frac{\gamma D}{2}\Delta \varphi^2+\frac{\lambda D}{6}\Delta \varphi^3, \] where \(\tau\) is the reduced temperature, \(\gamma\) and \(\lambda>0\) are phenomenological constants, \(D\) is the diffusion coefficient (relaxation coefficient). The reduction of the LB model to a system of ODEs on the center manifold generated by the instable modes at the introduced critical parameter \(\eta_c\) allows to prove the main result of the article.