Pattern formation below criticality forced by noise
type: Item
instance of: scholarly article
title: Pattern formation below criticality forced by noise
zbMATH Open document ID: 1018.60064
DOI: 10.1007/PL00012626
author: D. Blömker
author: Stanislaus Maier-Paape
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 2003-03-27T00:00:00Z
review text: A stochastic partial differential equation of the Swift-Hohenberg type which is a simplified model for fluids at the convective instability is considered. The authors take a different approach that describes directly the dynamical behaviour of most realizations. The paper is organized as follows. Section 2 provides the basic notions, definitions and assumptions needed in the sequel. In addition, it contains a precise formulation of the main linear theorem which is proved in Section 3. Here the technical theorems provided by Section 4 are intensively used. The extension of the theory to nonlinear equations is discussed in Section 5 and in the last Section 6 the new wavelength estimate is derived. Everywhere in this paper the stochastic perturbation has an additive form.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 1889258
zbMATH Keywords: stochastic partial differential equations
zbMATH Keywords: stochastic convolution
zbMATH Keywords: Swift-Hohenberg equation
reviewed by: Constantin Vârsan
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1889258