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Stability of pole solutions for planar propagating flames: I. Exact eigenvalues and eigenfunctions

Vaynblat, Dimitri and Matalon, Moshe (2000) Stability of pole solutions for planar propagating flames: I. Exact eigenvalues and eigenfunctions. SIAM Journal on Applied Mathematics, 60 (2). pp. 679-702. ISSN 0036-1399. https://resolver.caltech.edu/CaltechAUTHORS:VAYsiamjam00a

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Abstract

It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution corresponds to a steadily propagating cusp-like structure commonly observed in experiments. In this work we investigate the linear stability of these equilibrium states-the steady coalescent pole solutions. In previous similar studies, either a truncated linear system was numerically solved for the eigenvalues or the initial value problem for the linearized PDE was numerically integrated in order to examine the evolution of initially small disturbances in time. In contrast, our results are based on the exact analytical expressions for the eigenvalues and corresponding eigenfunctions. In this paper we derive the expressions for the eigenvalues and eigenfunctions. Their properties and the implication on the stability of pole solutions is discussed in a paper which will appear later.


Item Type:Article
Additional Information:© 2000 Society for Industrial and Applied Mathematics. Received by the editors October 29, 1998; accepted for publication March 23, 1999; published electronically February 2, 2000. This research was partially supported by the National Science Foundation under grants DMS9703716 and CTS9521022.
Subject Keywords:flame front, pole decomposition, coalescent pole solution, stability, eigenvalues and eigenfunctions, wrinkled premixed flames, non-linear analysis, hydrodynamic instability, cellular nature, laminar flames, equation, decomposition, dynamics, fronts
Issue or Number:2
Record Number:CaltechAUTHORS:VAYsiamjam00a
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:VAYsiamjam00a
Alternative URL:http://dx.doi.org/10.1137/S0036139998346439
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:858
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:31 Oct 2005
Last Modified:02 Oct 2019 22:37

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