Galloping instability of viscous shock waves

  • Date: 11/14/2006

Benjamin Texier (Paris 7)


University of British Columbia


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