Ferroelectric ceramics exhibit a spontaneous electric polarization that can be reversed under the application of an electrical or mechanical loading. The method of choice to model the evolution of polarization domains are diffuse-interface models (also called phase-field models), most of them being based on the Allen-Cahn equation. The latter assumes, unlike experimental evidence, a linear relation between the velocity of domain walls and their conjugate driving force. In this work, we develop an alternative phase-field formulation that accounts for the non-linear kinetics of domain walls, an important feature with regards to rate effects in ferroelectrics.