  Combining work of Serre and Zumbrun, Benzoni-Gavage, Serre, and Zumbrun, and
Texier and Zumbrun, we propose as a mechanism for the onset of cellular
instability of viscous shock and detonation waves in a finite-cross-section
duct the violation of the refined planar stability condition of Zumbrun--Serre,
a viscous correction of the inviscid planar stability condition of Majda. More
precisely, we show for a model problem involving flow in a rectangular duct
with artificial periodic boundary conditions that transition to
multidimensional instability through violation of the refined stability
condition of planar viscous shock waves on the whole space generically implies
for a duct of sufficiently large cross-section a cascade of Hopf bifurcations
involving more and more complicated cellular instabilities.
  The refined condition is numerically calculable as described in
Benzoni-Gavage--Serre-Zumbrun.
