Gelfand-type problem for turbulent jets

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Gordon, Peter V.¹  Moroz, Vitaly²  Nazarov, Fedor¹ 

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Swansea Univ, Computat Foundry, Dept Math, Fabian Way, Swansea SA1 8EN, W Glam, Wales

关键词: Gelfand problem;    Strong advection;    Extremal solutions;    Stable solutions;    Thermal explosion;   

DOI  :  10.1016/j.jde.2020.04.026

来源: Elsevier

【 摘 要 】

We consider the model of auto-ignition (thermal explosion) of a free round reactive turbulent jet intro-duced in [11]. This model falls into the general class of Gelfand-type problems and constitutes a boundary value problem for a certain semi-linear elliptic equation that depends on two parameters: alpha characterizing the flow rate and lambda (Frank-Kamenetskii parameter) characterizing the strength of the reaction. Similarly to the classical Gelfand problem, this equation admits a solution when the Frank-Kamenetskii parameter lambda does not exceed some critical value lambda* (alpha) and admits no solutions for larger values of lambda. We obtain the sharp asymptotic behavior of the critical Frank-Kamenetskii parameter in the strong flow limit (alpha >> 1). We also provide a detailed description of the extremal solution (i.e., the solution corresponding to lambda*) in this regime. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free