Instabilities in a combustion model with two free interfaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:268

Article

Addona, D.¹  Brauner, C-M^2,3  Lorenzi, L.⁴  Zhang, W.^5,6 

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via R Cozzi 55, I-20125 Milan, Italy

[2] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

[3] Univ Bordeaux, Inst Math Bordeaux, F-33405 Talence, France

[4] Univ Palma, Dipartimento Sci Matemat Fis & Informat, Plesso Matemat, Parco Area Sci 53-A, I-43124 Palma, Italy

[5] East China Univ Technol, Sch Sci, Nanchang 330013, Peoples R China

[6] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China

关键词: Free boundary problems with two free interfaces;    Traveling wave solutions;    Instability;    Fully nonlinear parabolic problems;    Analytic semigroups;    Dispersion relation;   

DOI  :  10.1016/j.jde.2019.10.015

来源: Elsevier

【 摘 要 】

We study in a strip of R-2 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 Le(c) of the Lewis number Le, such that the one-dimensional, planar, solution is unstable for 0 < Le < Le(c). Some numerical simulations confirm the analysis. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free