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Instability of free interfaces in premixed flame propagation
Full text linkIn this survey, we are interested in the instability of flame fronts regarded as free interfaces. We successively consider a classical Arrhenius kinetics (thin flame) and a stepwise ignition-tempera ture kinetics (thick flame) with two free interfaces. A general method initially developed for thin flame problems subject to interface jump conditions is proving to be an effective strategy for smoother thick flame systems. It relies on the elimination of the free interface(s) and reduction to a fully nonlinear parabolic problem. The theory of analytic semigroups is a key tool to study the linearized operators
Computation of bifurcated branches in a free boundary problem arising in combustion theory
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On the - model of cellular flames: existence in the large and asymptotics.
No full textWe consider the κ-θ model of flame front dynamics introduced in [6]. We show that a space-periodic problem for the latter system of two equations is globally well-posed. We prove that near the instability threshold the front is arbitrarily close to the solution of the Kuramoto-Sivashinsky equation on a fixed time interval if the evolution starts from close configurations. The dynamics generated by the model is illustrated by direct numerical simulation
STABILITY OF TRAVELING WAVE SOLUTIONS IN A CREDIT RATING MIGRATION FREE BOUNDARY PROBLEM
No full textIn this paper, we study the stability of traveling wave solutions arising from a credit rating migration problem with a free boundary, After some transformations, we turn the free boundary problem into a fully nonlinear parabolic problem on a fixed domain and establish a rigorous stability analysis of the equilibrium in an exponentially weighted function space. It implies the convergence of the discounted value of bonds that stands as an attenuated traveling wave solution
Instabilities in a combustion model with two free interfaces
Full text linkWe study in a strip of R2 a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter interface presents an additional difficulty because the non-degeneracy condition is not met. We turn the system to a fully nonlinear problem which is thoroughly investigated. When the width l of the strip is sufficiently large, we prove the existence of a critical value Lec of the Lewis number Le, such that the one-dimensional, planar, solution is unstable for
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