Simultaneous global inviscid Burgers flows with periodic Poisson forcing

We study the inviscid Burgers equation on the circle T := R/Z forced by the spatial derivative of a Poisson point process on R × T. We construct global solutions with mean θ simultaneously for all θ ∈ R, and in addition construct their associated global shocks (which are unique except on a countable set of θ). We then show that as θ changes, the solution only changes through the movement of the global shock, and give precise formulas for this movement. This can be seen as an analogue of previous results by the author and Yu Gu in the viscous case with white-in-time forcing, which related the derivative of the solution in θ to the density of a particle diffusing in the Burgers flow

Duke Scholars

Author Alexander J Dunlap Mathematics