Limit theorem for the statistical solution of Burgers equation
type: Item
instance of: scholarly article
title: Limit theorem for the statistical solution of Burgers equation
zbMATH Open document ID: 0961.60034
DOI: 10.1016/S0304-4149(99)00002-2
published in: Stochastic Processes and their Applications
publication date: 2001-01-17T00:00:00Z
review text: The Cole-Hopf solutions of the one-dimensional Burgers equation of the form \[ \partial _tu+u\partial _xu=\frac {\nu}{2}\partial ^2_{xx}u,\quad x\in \mathbb R,\;t>0, \] are studied, where \(\nu >0\) is the viscosity and the initial value \(u(x,0)=-d\xi (x)/dx\) is given, in the case when the initial value is a functional of a Gaussian process. By means of the Gauss chaos decomposition limit results of the type of the ``Gaussian scenario'' are obtained with new normalization factors.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1554312
zbMATH Keywords: Burgers equation
zbMATH Keywords: chaos decomposition
zbMATH Keywords: Hopf-Cole solution
author: Azzouz Dermoune
author: Said Hamadène
author: Youssef Ouknine
MaRDI profile type: Publication
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full work available at URL: s0304-4149(99)00002-2
OpenAlex ID: W2051230326
description: scientific article; zbMATH DE number 1554312