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

Dimitri Vaynblat, Moshe Matalon

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)679-702
Number of pages24
JournalSIAM Journal on Applied Mathematics
Volume60
Issue number2
DOIs
StatePublished - Jan 1 2000

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Eigenvalues and Eigenfunctions
Flame
Eigenvalues and eigenfunctions
Pole
Poles
Equilibrium State
Eigenvalue
Nonlinear PDE
Stability of Equilibria
Linear Stability
Cusp
Initial Value Problem
Eigenfunctions
Initial value problems
Disturbance
Unstable
Linear Systems
Linear systems
Experiment
Experiments

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Stability of pole solutions for planar propagating flames : I. Exact eigenvalues and eigenfunctions. / Vaynblat, Dimitri; Matalon, Moshe.

In: SIAM Journal on Applied Mathematics, Vol. 60, No. 2, 01.01.2000, p. 679-702.

Research output: Contribution to journalArticle

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