  Following the approach pioneered by Eckhaus, Mielke, Schneider, and others
for reaction diffusion systems [E, M1, M2, S1, S2, SZJV], we systematically
derive formally by multiscale expansion and justify rigorously by
Lyapunov-Schmidt reduction amplitude equations describing Turing-type
bifurcations of general reaction diffusion convection systems. Notably, our
analysis includes also higher-order, nonlocal, and even certain semilinear
hyperbolic systems.
