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.

从理论和计算的角度研究了反应扩散Landau–Khalatnikov方程的初边值问题，该方程用于描述铁电体的极化转换。证明了初边值问题的弱解的存在性和唯一性。构造了具有二阶精度的绝对稳定的单调数值方案，并结合了迭代程序。进行了具有一阶相变的铁电体极化滞后的数值模拟。将基于模型的不同修改而获得的计算结果与实验数据进行比较。为了充分描述铁电体中的极化转换，显示了扩散项及其缩放效应的重要作用。