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

  • Daniel ConusEmail author
  • Mathew Joseph
  • Davar Khoshnevisan
  • Shang-Yuan Shiu
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

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).

Keywords

Intermittency The stochastic wave equation Chaos 

Notes

Acknowledgements

An anonymous referee read this paper quite carefully and made a number of critical suggestions and corrections that have improved the paper. We thank him or her wholeheartedly.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Daniel Conus
    • 1
    Email author
  • Mathew Joseph
    • 2
    • 3
  • Davar Khoshnevisan
    • 2
  • Shang-Yuan Shiu
    • 4
  1. 1.Department of MathematicsLehigh UniversityBethlehemUSA
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA
  3. 3.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUK
  4. 4.Department of MathematicsNational Central UniversityJhongli CityTaiwan

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