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Nonlinear stochastic evolution equations of second order with damping


Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.

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The authors would like to thank Raphael Kruse (Berlin) for helpful discussions and comments and to the referees for their careful reading and helpful suggestions.

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Correspondence to Etienne Emmrich.

Additional information

This work has been partially supported by the Collaborative Research Center 910, which is funded by the German Science Foundation.

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Emmrich, E., Šiška, D. Nonlinear stochastic evolution equations of second order with damping. Stoch PDE: Anal Comp 5, 81–112 (2017). https://doi.org/10.1007/s40072-016-0082-1

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  • Stochastic evolution equation of second order
  • Monotone operator
  • Full discretization
  • Convergence
  • Existence
  • Uniqueness

Mathematics Subject Classification

  • 60H15
  • 47J35
  • 60H35
  • 65M12