Year: 2016
Author: Claude-Michel Brauner
Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v49n2.16.01
Journal of Mathematical Study, Vol. 49 (2016), Iss. 2 : pp. 93–110
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Free interface combustion theory Kuramoto-Sivashinsky equation instability fully nonlinear parabolic equation.