  Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion
systems, we justify rigorously the Eckhaus stability criterion for stability of
convective Turing patterns, as derived formally by complex Ginzburg-Landau
approximation [SS, NW, WZ]. Notably, our analysis includes also higher-order,
nonlocal, and even certain semilinear hyperbolic systems.
