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White noise driven quasilinear SPDEs with reflection
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  • Published: March 1992

White noise driven quasilinear SPDEs with reflection

  • D. Nualart1 &
  • E. Pardoux2 

Probability Theory and Related Fields volume 93, pages 77–89 (1992)Cite this article

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  • 100 Citations

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Summary

We study reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solutionu(x, t) is strictly positive it obeys the equation, and at a point (x, t) whereu(x, t) is zero we add a force in order to prevent it from becoming negative. This can be viewed as an extension both of one-dimensional SDEs reflected at 0, and of deterministic variational inequalities. An existence and uniqueness result is proved, which relies heavily on new results for a deterministic variational inequality.

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Author information

Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    D. Nualart

  2. Mathématiques, URA 225, Université de Provence, F-13331, Marseille Cedex 3, France

    E. Pardoux

Authors
  1. D. Nualart
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  2. E. Pardoux
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Additional information

INRIA

Partially supported by DRET under contract 901636/A000/DRET/DS/SR

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Cite this article

Nualart, D., Pardoux, E. White noise driven quasilinear SPDEs with reflection. Probab. Th. Rel. Fields 93, 77–89 (1992). https://doi.org/10.1007/BF01195389

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  • Received: 12 April 1991

  • Revised: 11 December 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01195389

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Mathematics Subject Classification

  • 60H15
  • 35H60
  • 35R45
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