On the long-time behavior of ferroelectric systems

This paper presents a new model for the ferroelectric behavior of materials. The usual Maxwell's equations are supplemented with a constitutive relation in which the electric displacement equals a constant times the: electric field plus an internal polarization variable. The latter evolves according to an internal set of Maxwell equations. This model is suggested by one presented by one of the authors for elastic behavior with phase change. The model admits hysteretic behavior. The asymptotic behavior with respect to time is studied and it is shown that the system tends to a steady state in which the polarization is governed by a nonlinear elliptic equation. It is shown that this equation has multiple solutions which correspond to microstructure. (C) 1999 Elsevier Science B.V. All rights reserved.