  In this paper we consider a semilinear parabolic equation in an infinite
cylinder. The spatially varying nonlinearity is such that it connects two
(spatially independent) bistable nonlinearities in a compact set in space. We
prove that, given such a setting, a traveling wave obeying the equation with
the one bistable nonlinearity and starting at the respective side of the
cylinder, will converge to a traveling wave solution prescribed by the
nonlinearity on the other side.
