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Numerical simulation of a point-source initiated flame ball with heat losses

Jacques AudounetJean-Michel RoquejoffreHélène Rouzaud — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.

Travelling graphs for the forced mean curvature motion in an arbitrary space dimension

Régis MonneauJean-Michel RoquejoffreViolaine Roussier-Michon — 2013

Annales scientifiques de l'École Normale Supérieure

We construct travelling wave graphs of the form z = - c t + φ ( x ) , φ : x N - 1 φ ( x ) , N 2 , solutions to the N -dimensional forced mean curvature motion V n = - c 0 + κ ( c c 0 ) with prescribed asymptotics. For any 1 -homogeneous function φ , viscosity solution to the eikonal equation | D φ | = ( c / c 0 ) 2 - 1 , we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by  φ . We also describe φ in terms of a probability measure on  § N - 2 .

Speed-up of reaction-diffusion fronts by a line of fast diffusion

Henri BerestyckiAnne-Charline CoulonJean-Michel RoquejoffreLuca Rossi

Séminaire Laurent Schwartz — EDP et applications

In these notes, we discuss a new model, proposed by H. Berestycki, J.-M. Roquejoffre and L. Rossi, to describe biological invasions in the plane when a strong diffusion takes place on a line. This model seems relevant to account for the effects of roads on the spreading of invasive species. In what follows, the diffusion on the line will either be modelled by the Laplacian operator, or the fractional Laplacian of order less than 1. Of interest to us is the asymptotic speed of spreading in the direction...

Existence of pulsating waves in a model of flames in sprays

Peter ConstantinKomla DomelevoJean-Michel RoquejoffreLenya Ryzhik — 2006

Journal of the European Mathematical Society

A one-dimensional system describing the propagation of low Mach number flames in sprays is studied. We show that pulsating waves may exist when the droplet distribution in the unburnt region is spatially periodic. The range of possible propagation speeds may be either bounded or unbounded, depending on the threshold temperatures of the burning and vaporization rates.

Variational problems with free boundaries for the fractional Laplacian

Luis CaffarelliJean-Michel RoquejoffreYannick Sire — 2010

Journal of the European Mathematical Society

We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.

Numerical simulation of a point-source initiated flame ball with heat losses

Jacques AudounetJean-Michel RoquejoffreHélène Rouzaud — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.

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