EVENT DETAILS AND ABSTRACT

Title: Hopf bifurcation and galloping instability of detonation waves
Speaker: Professor Kevin Zumbrun
Speaker Info: Indiana University
Brief Description:
Special Note:
Abstract:

Transition to longitudinal instability of detonation waves is typified by ``galloping'' or ``pulsating'' behavior, appearing as time-periodic perturbations of the wave. We discuss from several points of view the rigorous characterization of this phemonenon, within the context of the reactive Navier-Stokes equations, as a relative Poincare-Hopf bifurcation with respect to the underlying group invariance of translation. The main mathematical issue from the point of view of abstract bifurcation theory is the absence of a spectral gap between bifurcating modes and essential spectrum of the linearized operator about the wave.