Galloping instability of viscous shock waves

  • Date: 11/14/2006
Lecturer(s):

Benjamin Texier (Paris 7)

Location: 

University of British Columbia

Topic: 

This is joint work with Kevin Zumbrun (Indiana University). Motivated
by physical and numerical observations of time oscillatory galloping,
spinning, and cellular instabilities of detonation waves, we study
Poincare--Hopf bifurcation of traveling-wave solutions of viscous
conservation laws. The main difficulty is the absence of a spectral gap
between oscillatory modes and essential spectrum, preventing standard
reduction to a finite-dimensional center manifold. We overcome this by
direct Lyapunov--Schmidt reduction, using detailed pointwise bounds on
the linearized solution operator.

Other Information: 

DG-MP-PDE Seminar 2006

Sponsor: 

pims