  A one dimensional kinetic Ising model at a finite temperature on a
semi-infinite lattice with time varying boundary spins is considered. Exact
expressions for the expectation values of the spin at each site are obtained,
in terms of the time dependent boundary condition and the initial conditions.
The solution consists of a transient part which is due to the initial
condition, and a part driven by the boundary. The latter is an evanescent wave
when the boundary spin is oscillating harmonically. Low- and high-frequency
limits are investigated with greater detail. The total magnetization of the
lattice is also obtained. It is seen that for any arbitrary rapidly varying
boundary conditions, this total magnetization is equal to the the boundary spin
itself, plus essentially the time integral of the boundary spin. A nonuniform
model is also investigated.
