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From crystal steps to continuum laws:Behavior near large facets in one dimension
Crystal surface Epitaxial relaxation Self-similar solution Burton–Cabrera–Frank (BCF) model Facet Macroscopic limit
2015/10/16
The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by exp...
Slow time behavior of the semidiscrete Perona-Malik scheme in dimension one
Perona-Malik equation semidiscrete scheme forward-backward parabolic equation
2011/2/24
We consider the long time behavior of the semidiscrete scheme for the Perona-Malik equation in dimension one. We prove that approximated solutions converge, in a slow time scale, to solutions of a lim...