  We consider a system of reaction-diffusion equations in a bounded interval of
the real line, with emphasis on the metastable dynamics, whereby the
time-dependent solution approaches its steady state in an asymptotically
exponentially long time interval as the viscosity coefficient $\varepsilon>0$
goes to zero. To rigorous describe such behavior, we analyze the dynamics of
solutions in a neighborhood of a one-parameter family of approximate steady
states, and we derive an ODE for the position of the internal interfaces.
