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. © 2008 Springer-Verlag.
Soft and hard wall in a stochastic reaction diffusion equation / BERTINI MALGARINI, Lorenzo; Stella, Brassesco; Butta', Paolo. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - STAMPA. - 190:2(2008), pp. 307-345. [10.1007/s00205-008-0154-0]
Soft and hard wall in a stochastic reaction diffusion equation
BERTINI MALGARINI, Lorenzo;BUTTA', Paolo
2008
Abstract
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. © 2008 Springer-Verlag.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.