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| 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 stable equilibrium configuration in an asymptotically exponentially long time interval as the viscosity coefficient $\varepsilon>0$ goes to zero. In particular, we describe the phenomenon of the slow convergence of a layered solution into a patternless steady state. 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. |
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