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Resonant gas dynamics and a degenerate, quasilinear Schrodinger equation
PDE & Applied Mathematics| Speaker: | John Hunter, UC Davis |
| Location: | 3106 MSB |
| Start time: | Mon, Apr 9 2018, 3:10PM |
Description
We derive a degenerate, quasilinear Schrodinger equation that describes
the resonant reflection of very weak sound waves off an entropy wave in
one-dimensional gas dynamics. This PDE is a dispersive analog of the
parabolic porous medium equation. Numerical solutions of the PDE show an
interesting front propagation phenomenon, but many analytical questions,
including local well-posedness of the PDE and the front structure remain
open. We will discuss some of these question and consider the
possibility of using Whitham modulation theory to understand front
propagation. This is joint work with Evan Smothers.