Display Abstract

Title Slow motion of interfaces for a system of reaction-diffusion equations

Name Marta Strani
Country France
Email martastrani@gmail.com
Submit Time 2014-02-28 11:38:26
Special Session 12: Complexity 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 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.