  Extending work of Texier and Zumbrun in the semilinear non-re ection
symmetric case, we study O(2) transverse Hopf bifurcation, or \cellular
instability," of viscous shock waves in a channel, for a class of quasilinear
hyperbolic{parabolic systems including the equations of thermoviscoelasticity.
The main difficulties are to (i) obtain Fr'echet differentiability of the
time-T solution operator by appropriate hyperbolic{parabolic energy estimates,
and (ii) handle O(2) symmetry in the absence of either center manifold
reduction (due to lack of spectral gap) or (due to nonstandard quasilinear
hyperbolic-parabolic form) the requisite framework for treatment by spatial
dynamics on the space of time-periodic functions, the two standard treatments
for this problem. The latter issue is resolved by Lyapunov{Schmidt reduction of
the time-T map, yielding a four-dimensional problem with O(2) plus approximate
S1 symmetry, which we treat \by hand" using direct Implicit Function Theorem
arguments. The former is treated by balancing information obtained in
Lagrangian coordinates with that from an augmented system. Interestingly, this
argument does not apply to gas dynamics or magnetohydrodynamics (MHD), due to
the infinite-dimensional family of Lagrangian symmetries corresponding to
invariance under arbitrary volume-preserving diffeomorphisms.
