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Reaction-diffusion-convection problems in unbounded cylinders. (Problèmes de réaction-diffusion-convection dans des cylindres non bornés.) (French. Abridged English version) Zbl 0991.35044
Summary: 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 and to prove existence of convective waves. Finally, we make some conclusions about the possible appearance of a “convective instability”.

MSC:
35K57 Reaction-diffusion equations
35Q30 Navier-Stokes equations
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
35B32 Bifurcations in context of PDEs
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76R99 Diffusion and convection
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