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Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients | Patrick W Dondl
; Michael Scheutzow
; | Date: |
28 Feb 2011 | Abstract: | We consider a model for the propagation of a driven interface through a
random field of obstacles. The evolution equation, commonly referred to as the
Quenched Edwards-Wilkinson model, is a semilinear parabolic equation with a
constant driving term and random nonlinearity to model the influence of the
obstacle field. For the case of isolated obstacles centered on lattice points
and admitting a random strength with exponential tails, we show that the
interface propagates with a finite velocity for sufficiently large driving
force. The proof consists of a discretization of the evolution equation and a
supermartingale estimate akin to the study of branching random walks. | Source: | arXiv, 1102.5691 | Services: | Forum | Review | PDF | Favorites |
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