Bifurcation of Symmetric Domain Walls for the Benard-Rayleigh Convection Problem

We prove the existence of domain walls for the Benard-Rayleigh convection problem. Our approach relies upon a spatial dynamics formulation of the hydrodynamic problem, a center manifold reduction, and a normal forms analysis of an eight-dimensional reduced system. Domain walls are constructed as heteroclinic solutions connecting suitably chosen periodic solutions of this reduced system.