Thumbnail Image
Publication

Random Nonlinear Wave Equations: Propagation of Singularities

Carmona, Rene
; 
Nualart, David
Citations
Altmetric:
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176991784.
Date
1988-02-06
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics (IMS)
Collections
Mathematics Scholarly Works
Show all metadata
Files
Thumbnail Image
NualartD_AP_16(2)730.pdf
Adobe PDF, 1.39 MB
Research Projects
Organizational Units
Journal Issue
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. http://dx.doi.org/10.1214/aop/1176991784.
URI
https://hdl.handle.net/1808/17065
DOI
10.1214/aop/1176991784
Embedded videos