Abstract
Singular limit is investigated for reaction-diffusion equations with an additive noise in a bounded domain of ℝ2. The solution converges to one of the two stable phases {+1, −1} determined from the reaction term; accordingly a phase separation curve is generated in the limit. We shall derive a randomly perturbed motion by curvature for the dynamics of the phase separation curve.
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Funaki, T. Singular limit for stochastic reaction-diffusion equation and generation of random interfaces. Acta Mathematica Sinica 15, 407–438 (1999). https://doi.org/10.1007/BF02650735
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DOI: https://doi.org/10.1007/BF02650735