  We study the Ising-Bloch bifurcation in two systems, the Complex Ginzburg
Landau equation (CGLE) and a FitzHugh Nagumo (FN) model in the presence of
spatial inhomogeneity introduced by Dirichlet boundary conditions. It is seen
that the interaction of fronts with boundaries is similar in both systems,
establishing the generality of the Ising-Bloch bifurcation. We derive reduced
dynamical equations for the FN model that explain front dynamics close to the
boundary. We find that front dynamics in a highly non-adiabatic (slow front)
limit is controlled by fixed points of the reduced dynamical equations, that
occur close to the boundary.
