Local Existence and Uniqueness for a Two-Dimensional Surface Growth Equation With Space-Time White Noise

  • We study local existence and uniqueness for a surface growth model with space-time white noise in 2D. Unfortunately, the direct fixed-point argument for mild solutions fails here, as we do not have sufficient regularity for the stochastic forcing. Nevertheless, one can give a rigorous meaning to the stochastic PDE and show uniqueness of solutions in that setting. Using spectral Galerkin method and any other types of regularization of the noise, we obtain always the same solution.

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Author:Dirk BlömkerGND, Marco RomitoORCiD
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/2389
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2013-14)
Year of first Publication:2013
Publishing Institution:Universität Augsburg
Release Date:2013/07/17
Tag:local existence and uniqueness; surface growth model; regularization of noise; fixed point argument; mild solution
GND-Keyword:Stochastische partielle Differentialgleichung; Wachstumsmodell; Weißes Rauschen; Galerkin-Methode
Erschienen in Stochastic Analysis and Applications, 31, 6, S. 1049-1076, https://doi.org/10.1080/07362994.2013.829003
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand