Open Access System for Information Sharing

Login Library

 

Article
Cited 13 time in webofscience Cited 14 time in scopus
Metadata Downloads

A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs SCIE SCOPUS

Title
A Macroscopic Multifractal Analysis of Parabolic Stochastic PDEs
Authors
Khoshnevisan, DavarKim, KunwooXiao, Yimin
Date Issued
2018-05
Publisher
SPRINGER
Abstract
It is generally argued that the solution to a stochastic PDE with multiplicative noise-such as , where denotes space-time white noise-routinely produces exceptionally-large peaks that are "macroscopically multifractal." See, for example, Gibbon and Doering (Arch Ration Mech Anal 177:115-150, 2005), Gibbon and Titi (Proc R Soc A 461:3089-3097, 2005), and Zimmermann et al. (Phys Rev Lett 85(17):3612-3615, 2000). A few years ago, we proved that the spatial peaks of the solution to the mentioned stochastic PDE indeed form a random multifractal in the macroscopic sense of Barlow and Taylor (J Phys A 22(13):2621-2626, 1989; Proc Lond Math Soc (3) 64:125-152, 1992). The main result of the present paper is a proof of a rigorous formulation of the assertion that the spatio-temporal peaks of the solution form infinitely-many different multifractals on infinitely-many different scales, which we sometimes refer to as "stretch factors." A simpler, though still complex, such structure is shown to also exist for the constant-coefficient version of the said stochastic PDE.
URI
https://oasis.postech.ac.kr/handle/2014.oak/94688
DOI
10.1007/s00220-018-3136-6
ISSN
0010-3616
Article Type
Article
Citation
COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 360, no. 1, page. 307 - 346, 2018-05
Files in This Item:
There are no files associated with this item.

qr_code

  • mendeley

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Related Researcher

Researcher

김건우KIM, KUNWOO
Dept of Mathematics
Read more

Views & Downloads

Browse