Intermittency and chaos for a stochastic non-linear wave equation in dimension 1

Details Intermittency and chaos for a stochastic non-linear wave equation in dimension 1 Intermittency and chaos for a stochastic non-linear wave equation in dimension 1

2011-12-08

arxiv.org/abs/1112.1909v1

Mathematics

Probability

23 pages

Scientific paper

We consider a non-linear stochastic wave equation driven by space-time white noise in dimension 1. First of all, we state some results about the intermittency of the solution, which have only been carefully studied in some particular cases so far. Then, we establish a comparison principle for the solution, following the ideas of Mueller. We think it is of particular interest to obtain such a result for a hyperbolic equation. Finally, using the results mentioned above, we aim to show that the solution exhibits a chaotic behavior, in a similar way as was established by Conus, Joseph, and Khoshnevisan for the heat equation. We study the two cases where 1. the initial conditions have compact support, where the global maximum of the solution remains bounded and 2. the initial conditions are bounded away from 0, where the global maximum is almost surely infinite. Interesting estimates are also provided on the behavior of the global maximum of the solution.

Affiliated with

Also associated with

No associations

Rating

Intermittency and chaos for a stochastic non-linear wave equation in dimension 1 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intermittency and chaos for a stochastic non-linear wave equation in dimension 1, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intermittency and chaos for a stochastic non-linear wave equation in dimension 1 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-549126