  We present the analytical study of stability loss and evolution of domain
structure in inhomogeneous ferroelectric and ferroelastic samples for exactly
solvable models. The model assumes a short-circuited ferroelectric capacitor
(free ferroelastic) with two regions with slightly different critical
temperatures Tc1 Tc2, where Tc1-Tc2 << Tc1, Tc2. We show that even a tiny
inhomogeneity like 10-5 K results in splitting the system into domains below
the phase transition temperature. At T < Tc2 the domain width a is proportional
to (Tc1-T)/(Tc1-Tc2) and quickly increases with lowering temperature. The
minute inhomogeneities in Tc may result from structural (growth)
inhomogeneities, which are always present in real samples, and a similar role
can be played by inevitable temperature gradients.
