Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory

Kuramoto-Sivashinsky Equation and Free-Interface Models in Combustion Theory

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.

Author Details

Claude-Michel Brauner