Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory (Journal of Mathematical Study, 2016)
In combustion theory, a thin flame zone is usually replaced by a free interface.A very challenging problem is the derivation of a self-consistent equation for theflame front which yields a reduction of the dimensionality of the system. A paradigmis the Kuramoto-Sivashinsky (K-S) equation, which models cellular instabilities andturbulence phenomena. In this survey paper, we browse through a series of models inwhich one reaches a fully nonlinear parabolic equation for the free interface, involvingpseudo-differential operators. The K-S equation appears to be asymptotically thelowest order of approximation near the threshold of stability.