  We present the first analytical study of stability loss and evolution of
domain structure in inhomogeneous ferroelectric samples for exactly solvable
model. The model assumes a short-circuited capacitor with two regions with
slightly different critical temperatures Tc1 > Tc2, where Tc1-Tc2 << Tc1, Tc2.
Even a tiny inhomogeneity like 10-5 K may result 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.
