Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Tuesday, May 7, 2013 - 04:00 to 05:00

Location:

Kidd 364

Guest Speaker:

Institution:

Drexel University

Abstract:

In many dispersive equations, such as the KdV or Benjamin-Ono equations, the dispersive terms appear linearly. There are other equations, however, in which the dispersion enters nonlinearly; examples come from numerical analysis and geophysical applications, among other places. Equations with nonlinear, degenerate dispersion are known to exhibit a variety of non-analytic traveling waves, such as compactons, but for many such equations, the well-posedness theory has not been developed. We demonstrate both ill-posedness and well-posedness results for equations with degenerate dispersion; the well-posedness results are related to a study of the competition between dispersion and backwards diffusion in linear PDE, which we will discuss. This includes joint work with Gideon Simpson, J. Douglas Wright, and Dennis G. Yang.

Host: