  Recently spatial as well as temporal variations of the fine structure
constant alpha have been reported. We show that a "runaway domain wall", which
arises for the scalar field potential without minima, can account for such
variations simultaneously. The time variation is induced by a runaway potential
and the spatial variation is induced by the formation of a domain wall. The
model is consistent with the current cosmological data and can be tested by the
future experiments to test the equivalence principle.
