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.

Automated summary

The study proves the existence of domain walls for the Benard-Rayleigh convection problem through a spatial dynamics formulation, center manifold reduction, and normal forms analysis of a reduced system. Domain walls are constructed as heteroclinic solutions connecting periodically chosen solutions of the reduced system.