  Pattern formation mechanisms of a reaction-diffusion-advection system, with
one diffusivity, differential advection, and (Robin) boundary conditions of
Danckwerts type, are being studied. Pattern selection requires mapping the
domains of coexistence and stability of propagating or stationary nonuniform
solutions, which for the general case of far from instability onsets, is
conducted using spatial dynamics and numerical continuations. The selection is
determined by the boundary conditions which either preserve or destroy the
translational symmetry of the model. Accordingly, we explain the criterion and
the properties of stationary periodic states if the system is bounded and show
that propagation of nonlinear waves (including solitary) against the advective
flow corresponds to coexisting family that emerges nonlinearly from a distinct
oscillatory Hopf instability. Consequently, the resulting pattern selection is
qualitatively different from the symmetric finite wavenumber Turing or Hopf
instabilities.
