Reaction-Diffusion-Convection Problems in Unbounded Cylinders%$

The work is devoted to reaction-diffusion-convection problems in unbounded cylinders. We study the Fredholm property and properness of the corresponding elliptic operators and define the topological degree. Together with analysis of the spectrum of the linearized operators it allows us to study bifurcations of solutions, to prove existence of convective waves, and to make some conclusions about their stability.

Key words: reaction-diffusion, convection, Navier-Stokes equations, Fredholm operators, topological degree, bifurcations, stability.
2000 Mathematics Subject Classification: 35J25, 47A53, 47H11, 80A32.