Scaling limit solution of a fractional Burgers equation.
type: Item
instance of: scholarly article
title: Scaling limit solution of a fractional Burgers equation.
zbMATH Open document ID: 1053.60073
DOI: 10.1016/S0304-4149(00)00106-X
published in: Stochastic Processes and their Applications
publication date: 2004-11-26T00:00:00Z
review text: The fractional version of the heat equation \[ \frac {\partial Y}{\partial t}(t,z)= -\mu (I-\Delta )^{\alpha /2}(-\Delta )^{\gamma /2}Y(t,z),\quad (t,z)\in R_+\times R^d, \] is considered with the initial conditions either of the form \[ Y(0,z)= \exp \left \{\frac {-\xi (z)}{2\widetilde \mu }\right \}\quad\text{or}\quad Y(0,z)=\exp \left \{-\frac {\xi ^2(z)-1}{2\mu \sigma ^2}\right \} \] where \(\xi \) represents the fractional Riesz-Bessel motion. Fractional scaling limits of the classes of random fields defined as the Hopf-Cole transformations, in the mean square sense, of the solutions to the equation are studied for both types of initial conditions. The scaling limits are calculated via their spectral representations. The spectral properties of the limiting random field are determined by the scaling asymptotic properties of the convolution kernel of the Lévy semigroup and the initial velocity potential random field.
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G12
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 2119500
zbMATH Keywords: fractional Burgers equation
zbMATH Keywords: Hopf-Cole transformation
zbMATH Keywords: scaling limit
author: María D. Ruiz-Medina
author: J. M. Angulo
author: Vo V. Anh
MaRDI profile type: Publication
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full work available at URL: s0304-4149(00)00106-x
OpenAlex ID: W2005435055
Wikidata QID: Q127859962
description: scientific article; zbMATH DE number 2119500