The main conclusion is that slow diffusion can act as a *stabilization
mechanism* in nonlinear reaction-diffusion equations. Patterns that are
unstable solutions of a scalar equation (1) can be stabilized
by the a priori negligible effects of coupling a slow diffusion equation
to this scalar problem (as in (3)). The general theory developed
in [4,3] can be used to determine whether this `control mechanism'
is effective; it can be applied to
large classes of singularly perturbed reaction-diffusion
equations, including the well-studied Gray-Scott and Gierer-Meinhardt models.
Moreover, the theory of [4,3] is formulated in the setting
of the Evans function approach. As a consequence, it is possible to
extend the method both to more general classes of `patterns' (including
multi-pulse and periodic patterns) and to more general systems than
two-component reaction-diffusion
equations in one spatial dimension [5].