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