Open Access
April, 1988 Random Nonlinear Wave Equations: Propagation of Singularities
Rene Carmona, David Nualart
Ann. Probab. 16(2): 730-751 (April, 1988). DOI: 10.1214/aop/1176991784


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.


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Rene Carmona. David Nualart. "Random Nonlinear Wave Equations: Propagation of Singularities." Ann. Probab. 16 (2) 730 - 751, April, 1988.


Published: April, 1988
First available in Project Euclid: 19 April 2007

zbMATH: 0643.60045
MathSciNet: MR929075
Digital Object Identifier: 10.1214/aop/1176991784

Primary: 60H15

Keywords: Brownian motions , Laws of the iterated logarithm , Random wave equations

Rights: Copyright © 1988 Institute of Mathematical Statistics

Vol.16 • No. 2 • April, 1988
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