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Some mathematical aspects of flame chaos and flame multiplicity

1986; Elsevier BV; Volume: 20; Issue: 1 Linguagem: Inglês

10.1016/0167-2789(86)90099-0

1872-8022

B. Nicolaenko,

Fluid Dynamics and Turbulent Flows

In these review lectures, we survey recent mathematical results on the low, finite-dimensional behavior of the Kuramoto-Sivashinsky equations; the latter model thermo-diffusive flame front instabilities. We outline how these PDE's are rigorously equivalent to a finite dynamical system (ongoing joint work with C. Foias, G. Sell, R. Temam). We also present an introduction to multiplicity phenomena in flames caused by chemical kinetics (the latter is an ongoing joint work with P. Clavin and P.C. Fife).