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Nonlinear stochastic evolution equations of second order with damping

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Abstract

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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Acknowledgments

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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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Etienne Emmrich

  2. School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King’s Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK

    David Šiška

Authors
  1. Etienne Emmrich
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  2. David Šiška
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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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  • DOI: https://doi.org/10.1007/s40072-016-0082-1

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