Initiation of subsonic detonation

Article type: Research Article

Authors: Brezis, H.^; | Kamin, S. | Sivashinsky, G.

Affiliations: Analyse Numérique, Université Pierre et Marie Curie, B.C. 187, 4 pl. Jussieu, 75252 Paris cedex 05, France E‐mail: brezis@ccr.jussieu.fr | Department of Mathematics, Rutgers University, Hill Center, 110 Frelinghuysen Rd., Piscataway, NJ 08854‐8019, USA | School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel E‐mail: kamin@math.tau.ac.il

Abstract: The long‐time behavior of the solution of the system \theta_\tau - \alpha \pi_\tau = \varOmega (\theta), \pi_\tau - \theta_\tau = \pi_{\xi\xi} is investigated. Such a system is related to the modeling of detonation waves subjected to strong hydraulic resistance. We establish that some initial conditions yield decay (failure of ignition) while for other initial conditions our results strongly suggest convergence to traveling waves (successful ignition).

Journal: Asymptotic Analysis, vol. 24, no. 1, pp. 73-90, 2000