| Abstract: |
| Gelfand problem is one of the canonical problems in the theory of
non-linear parabolic and elliptic PDEs .
This problem naturally arises in the Frank-Kamenetskii theory of
thermal explosion (autoignition) and describes an initial stage of
evolution of a temperature field in reactive materials and mixtures.
In this talk I will present a generalization of Gelfand problem for
the analysis of autoignition of reactive turbulent jets. I will
present both the derivation of this new model and its analysis. The
latter is performed using a combination of rigorous, formal asymptotic
and numerical techniques. It will be shown that similar to the
classical Gelfand problem an autoignition in jets occur exclusively
owing to the absence of self-similar temperature distribution which,
in mathematical terms, leads to loss of regularity (blow-up) of
underlying PDE. The detailed analysis of self-similar temperature
profiles will be presented and a sharp characterization of an
autoignition event in terms of principal geometric and physical
parameters of the problem will be given.
This a joint work with U.G. Hegde and M.C. Hicks of NASA Glenn Research Center. |
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