@Article{JMS-49-93, author = {Claude-Michel and Brauner and claude-michel.brauner@u-bordeaux.fr and 13316 and School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen 361005, Fujian, P.R. China and 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 = {

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.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v49n2.16.01}, url = {http://global-sci.org/intro/article_detail/jms/993.html} }