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Dynamics of SPDEs Driven by a Small Fractional Brownian Motion with Hurst Parameter Larger than 1/2

  • L. H. Duc
  • M. J. Garrido-Atienza
  • B. SchmalfußEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 229)

Abstract

We consider mild solutions of an SPDE driven by a time dependent perturbation which is Hölder continuous with a Hölder exponent larger than 1/2. In particular, such a perturbation is given by a fractional Brownian motion with Hurst parameter larger than 1/2. The coefficient in front of this noise is an operator with bounded first and second derivatives. We formulate conditions such that the equation has a unique pathwise solution. Further we investigate the globally exponential stability of the trivial solution.

Keywords

Stability, stochastic partial differential equations Fractional Brownian motion 

Mathematical Subject Classification 2010

Primary: 35B35 Secondary: 34A34 34F05 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • L. H. Duc
    • 1
    • 4
  • M. J. Garrido-Atienza
    • 2
  • B. Schmalfuß
    • 3
    Email author
  1. 1.Max-Planck-Institut Für Mathematik in den NaturwissenschaftenLeipzigGermany
  2. 2.Institute of MathematicsVietnam Academy of Science and TechnologyHanoiVietnam
  3. 3.Dpto. Ecuaciones Diferenciales y Análisis Numérico, Universidad de SevillaSevillaSpain
  4. 4.Institut für Mathematik, Friedrich Schiller Universität JenaJenaGermany

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