Homoclinic orbits of semilinear parabolic partial differential
equations can split under time-periodic forcing as for ordinary
differential equations. The stable and unstable manifold
may intersect transverse at persisting homoclinic points. The
size of the splitting is estimated
to be exponentially small of order exp$(-c/\epsilon)$ in the period $\epsilon$ of the forcing
with $\epsilon \rightarrow 0$.