TY - JOUR T1 - Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory AU - Brauner , Claude-Michel JO - Journal of Mathematical Study VL - 2 SP - 93 EP - 110 PY - 2016 DA - 2016/07 SN - 49 DO - http://doi.org/10.4208/jms.v49n2.16.01 UR - https://global-sci.org/intro/article_detail/jms/993.html KW - Free interface, combustion theory, Kuramoto-Sivashinsky equation, instability, fully nonlinear parabolic equation. AB -

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 the flame front which yields a reduction of the dimensionality of the system. A paradigm is the Kuramoto-Sivashinsky (K-S) equation, which models cellular instabilities and turbulence phenomena. In this survey paper, we browse through a series of models in which one reaches a fully nonlinear parabolic equation for the free interface, involving pseudo-differential operators. The K-S equation appears to be asymptotically the lowest order of approximation near the threshold of stability.