Title: Existence of weak and strong shock reflections
Speaker: Volker Elling
Speaker Info: University of Michigan
Brief Description:
Special Note:
Abstract:
When waves meet an oblique wall, they usually undergo regular reflection. But for shock waves there are two kinds of reflection, weak and strong. Moreover around 1875 Ernst Mach discovered another type of reflection, now named after him. Ever since, researchers have tried to find simple conditions predicting which type of reflection appears in particular circumstances. The most important candidates are the detachment, sonic, and von Neumann criteria. We prove counterexamples showing that both the sonic and detachment criterion are not universally correct. In particular there is a large variety of regular weak solutions with a transonic shock. To answer these questions, techniques from nonlinear elliptic theory are crucial. Jumps in the Fredholm index of a boundary-value problem in a corner domain play a crucial role.Date: Monday, October 19, 2009