Non-planar fronts in Boussinesq reactive flows

Henri Berestycki; Peter Constantin; Lenya Ryzhik

doi:10.1016/j.anihpc.2004.10.010

Non-planar fronts in Boussinesq reactive flows

Henri Berestycki, Peter Constantin, Lenya Ryzhik

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.

Original language	English (US)
Pages (from-to)	407-437
Number of pages	31
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	23
Issue number	4
DOIs	https://doi.org/10.1016/j.anihpc.2004.10.010
State	Published - 2006

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2004.10.010

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title = "Non-planar fronts in Boussinesq reactive flows",

abstract = "We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.",

author = "Henri Berestycki and Peter Constantin and Lenya Ryzhik",

note = "Funding Information: We thank Vitaly Volpert for explaining to us the results of [4] prior to its publication. We also thank Marta Lewicka for a careful reading of the preliminary version of the manuscript. This research was supported in part by the ASCI Flash center at the University of Chicago under DOE contract B341495. PC was partially supported by the NSF grant DMS-0202531, LR by NSF grant DMS-0203537, ONR grant N00014-02-1-0089 and an Alfred P. Sloan Fellowship.",

year = "2006",

doi = "10.1016/j.anihpc.2004.10.010",

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T1 - Non-planar fronts in Boussinesq reactive flows

AU - Berestycki, Henri

AU - Constantin, Peter

AU - Ryzhik, Lenya

N1 - Funding Information: We thank Vitaly Volpert for explaining to us the results of [4] prior to its publication. We also thank Marta Lewicka for a careful reading of the preliminary version of the manuscript. This research was supported in part by the ASCI Flash center at the University of Chicago under DOE contract B341495. PC was partially supported by the NSF grant DMS-0202531, LR by NSF grant DMS-0203537, ONR grant N00014-02-1-0089 and an Alfred P. Sloan Fellowship.

PY - 2006

Y1 - 2006

N2 - We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.

AB - We consider the reactive Boussinesq equations in a slanted cylinder, with zero stress boundary conditions and arbitrary Rayleigh number. We show that the equations have non-planar traveling front solutions that propagate at a constant speed. We also establish uniform upper bounds on the burning rate and the flow velocity for general front-like initial data for the Cauchy problem.

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SN - 0294-1449

VL - 23

SP - 407

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JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 4

ER -

Non-planar fronts in Boussinesq reactive flows

Abstract

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