| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1895602 | Journal of Geometry and Physics | 2014 | 8 Pages |
Abstract
The asymptotic behavior of solutions of the Burgers equation and its generalizations with initial value-boundary problem on a finite interval with constant boundary conditions is studied. Since it describes a dissipative medium, any initial profile will evolve to a time-invariant solution with the same boundary values. Yet there are three distinctive asymptotic processes: the initial profile may regularly decay to a smooth invariant solution; or a Heaviside-type gap develops through a dispersive shock and multi-oscillations; or an asymptotic limit is a stationary ‘sawtooth’ solution with periodical breaks of derivative.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Alexey Samokhin,