  An extension of the Kinetic Ising model with nonuniform coupling constants on
a one-dimensional lattice with boundaries is investigated, and the relaxation
of such a system towards its equilibrium is studied. Using a transfer matrix
method, it is shown that there are cases where the system exhibits a dynamical
phase transition. There may be two phases, the fast phase and the slow phase.
For some region of the parameter space, the relaxation time is independent of
the reaction rates at the boundaries. Changing continuously the reaction rates
at the boundaries, however, there is a point where the relaxation times begins
changing, as a continuous (nonconstant) function of the reaction rates at the
boundaries, so that at this point there is a jump in the derivative of the
relaxation time with respect to the reaction rates at the boundaries.
