Bunsen Flames as Steady Solutions of the Kuramoto–Sivashinsky Equation

Abstract

Rotationally invariant steady solutions of the Kuramoto–Sivashinsky equation in two space dimensions are studied. Specifically, conical solutions, i.e., solutions which tend to a constant slope at infinity, are sought after. These solutions in combustion theory have a physical interpretation as the Bunsen flames. The technique of rigorous estimates by computer is used to prove the existence of such solutions for all physically reasonable values of the slopes.