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Resonant gas dynamics and a degenerate, quasilinear Schrodinger equation

PDE and Applied Math Seminar

Speaker: John Hunter, UC Davis
Location: 3106 MSB
Start time: Mon, Apr 9 2018, 3:10PM

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.