The Annals of Probability

Random Nonlinear Wave Equations: Propagation of Singularities

Rene Carmona and David Nualart

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Abstract

We investigate the smoothness properties of the solutions of one-dimensional wave equations with nonlinear random forcing. We define singularities as anomalies in the local modulus of continuity of the solutions. We prove the existence of such singularities and their propagation along the characteristic curves. When the space variable is restricted to a bounded interval, we impose the Dirichlet boundary condition at the endpoints and we show how the singularities are reflected at the boundary.

Article information

Source
Ann. Probab., Volume 16, Number 2 (1988), 730-751.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991784

Digital Object Identifier
doi:10.1214/aop/1176991784

Mathematical Reviews number (MathSciNet)
MR929075

Zentralblatt MATH identifier
0643.60045

JSTOR
links.jstor.org

Subjects
Primary: 60H15: Stochastic partial differential equations [See also 35R60]

Keywords
Random wave equations Brownian motions laws of the iterated logarithm

Citation

Carmona, Rene; Nualart, David. Random Nonlinear Wave Equations: Propagation of Singularities. Ann. Probab. 16 (1988), no. 2, 730--751. doi:10.1214/aop/1176991784. https://projecteuclid.org/euclid.aop/1176991784


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