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Slow dynamics in reaction-diffusion systems

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 the 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 layered solutions localized far from the stable configurations of the system, and we derive an ODE for the position of the internal interfaces.