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Stochastic evolution of 2D crystals |
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| Authors: | Marcin Dudziński |
| Institution: | a Faculty of Applied Informatics and Mathematics, Warsaw University of Life Sciences, ul. Nowoursynowska 159, 02-776 Warsaw, Poland b Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile c Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland |
| Abstract: | We study a crystalline version of the modified Stefan problem in the plane. The feature of our approach is that, we consider a model with stochastic perturbations and assume the interfacial curve to be a polygon. The existence of solution to our stochastic system is established. Galerkin’s method is one of the main tools used in the proof of our assertion. |
| Keywords: | Stefan&rsquo s problem Crystalline motion Stochastic systems Galerkin&rsquo s method Itô &rsquo s formula Fixed point theorems |
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