  In this work we study the solvability of the initial boundary value problems,
which model a quasi-static nonlinear behavior of ferroelectric materials.
Similar to the metal plasticity the energy functional of a ferroelectric
material can be additively decomposed into reversible and remanent parts. The
remanent part associated with the remanent state of the material is assumed to
be a convex non-quadratic function $f$ of internal variables. In this work we
introduce the notion of the measure-valued solutions for the ferroelectric
models and show their existence in the rate-dependent case assuming the
coercivity of the function $f$. Regularizing the energy functional by a
quadratic positive definite term, which can be viewed as hardening, we show the
existence of measure-valued solutions for the rate-independent and
rate-dependent problems avoiding the coercivity assumption on $f$.
