Random non-linear wave equations: Smoothness of the solutions

Rene Carmona; David Nualart

doi:10.1007/BF00318783

Random non-linear wave equations: Smoothness of the solutions

Rene Carmona, David Nualart

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	469-508
Number of pages	40
Journal	Probability Theory and Related Fields
Volume	79
Issue number	4
DOIs	https://doi.org/10.1007/BF00318783
State	Published - Nov 1988
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Statistics and Probability
Statistics, Probability and Uncertainty

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10.1007/BF00318783

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title = "Random non-linear wave equations: Smoothness of the solutions",

abstract = "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.",

author = "Rene Carmona and David Nualart",

year = "1988",

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doi = "10.1007/BF00318783",

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pages = "469--508",

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AU - Carmona, Rene

AU - Nualart, David

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N2 - 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.

AB - 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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U2 - 10.1007/BF00318783

DO - 10.1007/BF00318783

M3 - Article

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 4

ER -

Random non-linear wave equations: Smoothness of the solutions

Abstract

All Science Journal Classification (ASJC) codes

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