|
|
|
|
|
|
|
|
Long-time stability of multidimensional viscous shock fronts, and hyperbolic-parabolic evolution systems
Shock- or compression-fronts are localized structures with stability properties that are typically very strong: a sonic boom, for instance, is a familiar example of a shock front with dramatically large amplitude that nonetheless propagates coherently over great distances. On the other hand, stability of shocks can fail in the presence of phase transition, chemical reaction, or ionization, in ways that for the moment remain mysterious. Thus to verify the experimentally observed stability within the context of compressible Navier-Stokes equations, and to understand when and how stability can fail, are questions of basic physical interest.
In this talk, we indicate some interesting functional analytic issues that arise in this problem due to the dual, hyperbolic-parabolic nature of the linearized equations, both at high and low frequencies. We then present recently-obtained necessary and sufficient spectral criteria for stability, in terms of an appropriate Evans function or "generalized spectral determinant". Finally, we discuss applications to the original physical questions posed above.
Thursday, November 18, 2004, 245 Altgeld Hall, 4 p.m.
Mathematics Colloquia homepage