Local existence and uniqueness for a two-dimensional surface growth\n equation with space--time white noise

2013/07/15 by Dirk Blömker, Blömker, Dirk, Marco Romito +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #60H15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1307.4034

openalex publication_date 2013/07/15 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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

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