Theoretical and numerical analysis of the Landau–Khalatnikov model of ferroelectric hysteresis

•An initial-boundary value problem for the Landau-Khalatnikov equation is studied.•The unique solvability of the initial-boundary value problem is proved.•A monotonic numerical scheme combined with an iterative procedure is constructed.•Numerical simulation of the polarization hysteresis in ferroelectrics is performed.•A scaling property of the diffusion term is shown. An initial-boundary value problem for the reaction-diffusion Landau–Khalatnikov equation applied to describe polarization switching in ferroelectrics is studied from both theoretical and computational points of view. The existence and uniqueness of a weak solution of the initial-boundary value problem are proved. An absolutely stable monotonic numerical scheme of the second-order accuracy combined with an iterative procedure is constructed. Numerical simulation of the polarization hysteresis in ferroelectrics with the first-order phase transition is performed. The results of the computations obtained on the base of different modifications of the model are compared with experimental data. An important role of the diffusion term and its scaling effect for an adequate description of the polarization switching in ferroelectrics are shown.