(Bounded) Traveling combustion fronts with degenerate kinetics. (February 2022)

• Record Type: Journal Article
• Authors: Alibaud, Nathaël; Namah, Gawtum
• Is Part Of: Nonlinear analysis. Volume 215(2022)
• Publication Date: 2022-02
• Subjects: 35R35 -- 80A25 -- 35C07 -- 35B10; Combustion -- Front propagation -- Hamilton–Jacobi equations -- Free boundary problems -- Nonplanar bounded traveling wave solutions -- Nonlinear degenerate kinetics -- Arrhenius law; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112541
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the propagation of a flame front in a solid periodic medium. It is governed by an equation of Hamilton–Jacobi type, whose front's velocity depends on the temperature via a nonlinear degenerate kinetic rate. The temperature solves a free boundary problem subject to boundary conditions depending on the front's velocity itself. We show the existence of nonplanar traveling wave solutions which are bounded and global. Previous results by the same authors (cf. Alibaud and Namah, 2017) were obtained for essentially positively lower bounded kinetics or eventually which have some very weak degeneracy. Here we consider very general degenerate kinetics, including for the first time those of Arrhenius type commonly used in physics.