Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 190, Issue 2, Pages 307-345Publisher
SPRINGER
DOI: 10.1007/s00205-008-0154-0
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- COFIN-MIUR
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We consider a stochastically perturbed reaction diffusion equation in a bounded interval, with boundary conditions imposing the two stable phases at the endpoints. We investigate the asymptotic behavior of the front separating the two stable phases, as the intensity of the noise vanishes and the size of the interval diverges. In particular, we prove that, in a suitable scaling limit, the front evolves according to a one-dimensional diffusion process with a non-linear drift accounting for a soft repulsion from the boundary. We finally show how a hard repulsion can be obtained by an extra diffusive scaling.
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