Intermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1

Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang Yuan Shiu

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

Consider a nonlinear stochastic wave equation driven by space-time white noise in dimension one. We discuss the intermittency of the solution, and then use those intermittency results in order to demonstrate that in many cases the solution is chaotic. For the most part, the novel portion of our work is about the two cases where (1) the initial conditions have compact support, where the global maximum of the solution remains bounded, and (2) the initial conditions are positive constants, where the global maximum is almost surely infinite. Bounds are also provided on the behavior of the global maximum of the solution in Case (2).

Original languageEnglish
Title of host publicationMalliavin Calculus and Stochastic Analysis
Subtitle of host publicationA Festschrift in Honor of David Nualart
PublisherSpringer New York LLC
Pages251-279
Number of pages29
ISBN (Print)9781461459057
DOIs
StatePublished - 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume34
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Keywords

  • Chaos
  • Intermittency
  • The stochastic wave equation

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