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
KW - combustion theory
KW - Kuramoto-Sivashinsky equation
KW - instability
KW - 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.