Sharp interface limit for invariant measures of a stochastic Allen‐Cahn equation

By Hendrik Weber. 2009

48 citations recorded by the source corpus.

The invariant measure of a one‐dimensional Allen‐Cahn equation with an additive space‐time white noise is studied. This measure is absolutely continuous with respect to a Brownian bridge with a density that can be interpreted as a potential energy term. We consider the sharp interface limit in this setup. In the right scaling this corresponds to a Gibbs‐type measure on a growing interval with decreasing temperature. Our main result is that in the limit we still see exponential convergence towards a curve of minimizers of the energy if the interval does not grow too fast. In the original scaling, the measure is concentrated on configurations with precisely one jump. © 2010 Wiley Periodicals, Inc.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/af083609e6b0fcebab938f500a533ab4001e79a0

Citations in the corpus

• The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “Some recent works on modeling and PDE analyses in this direction can be found in [166, 420, 421, 249, 346, 18, 20, 134, 133, 122, 363] and the references therein.”