Samokhin A. Numeric simulation of sawtooth solutions of the Burgers equation on a finite interval, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract)

From Geometry of Differential Equations
Jump to: navigation, search

Speaker: Alexey Samokhin

Title: Numeric simulation of sawtooth solutions of the Burgers equation on a finite interval

Abstract:
Properties of the solutions to the Burgers equation on a finite interval are studied. The initial value/boundary conditions model a periodic perturbation on the left boundary:

The asymptotics of the solution for this problem at coincides with the well known Fay solution

here is the Reynolds number, .

In particular, , which is the solution's average value over .

Not so for another asymptotics, at . The form of the solution retains the sawtooth profile yet its average over differs from and depends also on the perturbation amplitude . Interaction between two perturbations of different frequencies is discussed.

Slides: Samokhin A. Numeric simulation of sawtooth solutions of the Burgers equation on a finite interval (presentation at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic).pdf