The modified KdV-Burgers equation: shocks and traveling waves.

Michael Shearer, North Carolina State University

The MKdVB equation is a prototype equation for studying undercompressive shock wave solutions of hyperbolic conservation laws. In this informal talk, I will discuss traveling waves approximating undercompressive shocks, that fail the Lax entropy condition, and which can be calculated explicitly for this equation. Undercompressive waves can be incorporated into a theory of scalar conservation laws that competes with that developed by Lax, Oleinik and others around 40-50 years ago. In the colloquium talk, traveling waves for undercompressive shocks play a central role, but for the thin film equation, which has a different character from the MKdVB equation, and for which explicit calculations are not available.