@Article{JMS-49-2,
author = {Claude-Michel, Brauner},
title = {Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory},
journal = {Journal of Mathematical Study},
year = {2016},
volume = {49},
number = {2},
pages = {93--110},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v49n2.16.01},
url = {https://global-sci.com/article/87794/kuramoto-sivashinsky-equation-and-free-interface-models-in-combustion-theory}
}