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Random nonlinear wave equations: Smoothness of the solutions. (English) Zbl 0635.60073
We show existence and uniqueness for the solution of a one-dimensional wave equation with nonlinear 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 two parameters Wiener functionals.
Reviewer: R.Carmona

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G60 Random fields
Full Text: DOI
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