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Random non-linear wave equations: Smoothness of the solutions
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  • Published: November 1988

Random non-linear wave equations: Smoothness of the solutions

  • Rene Carmona1 &
  • David Nualart2 

Probability Theory and Related Fields volume 79, pages 469–508 (1988)Cite this article

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Summary

We show existence and uniqueness for the solution of a onedimensional wave equation with non-linear random forcing. Then we give sufficient conditions for the solution at a given time and a given point, to have a density and for this density to be smooth. The proof uses the extension of the Malliavin calculus to the two parameters Wiener functionals.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Irvine, 92717, Irvine, CA, USA

    Rene Carmona

  2. Facultat de Matematiques, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    David Nualart

Authors
  1. Rene Carmona
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  2. David Nualart
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Additional information

Partially supported by N.S.F. Grant DMS 850-3695

Partially supported by C.I.R.I.T.

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Carmona, R., Nualart, D. Random non-linear wave equations: Smoothness of the solutions. Probab. Th. Rel. Fields 79, 469–508 (1988). https://doi.org/10.1007/BF00318783

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  • Received: 01 March 1987

  • Revised: 09 February 1988

  • Issue Date: November 1988

  • DOI: https://doi.org/10.1007/BF00318783

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Keywords

  • Stochastic Process
  • Wave Equation
  • Probability Theory
  • Statistical Theory
  • Malliavin Calculus
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