Volume 49, Issue 2
Kuramoto-Sivashinsky Equation and Free-interface Models in Combustion Theory

Claude-Michel Brauner

J. Math. Study, 49 (2016), pp. 93-110.

Published online: 2016-07

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  • 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.
  • Keywords

Free interface combustion theory Kuramoto-Sivashinsky equation instability fully nonlinear parabolic equation

  • AMS Subject Headings

35K55, 35R37, 35B35, 35B40, 80A25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

claude-michel.brauner@u-bordeaux.fr (Claude-Michel Brauner)

  • BibTex
  • RIS
  • TXT
@Article{JMS-49-93, author = {Brauner , Claude-Michel}, 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} }
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.
Claude-Michel Brauner. (2019). Kuramoto-Sivashinsky Equation and Free-interface Models in Combustion Theory. Journal of Mathematical Study. 49 (2). 93-110. doi:10.4208/jms.v49n2.16.01
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