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Combustion Theory and Modelling Volume 2, 1998 - Issue 4
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Original Articles

Complex dynamics generated by a sharp interface model of self-propagating high-temperature synthesis

M FrankelDepartment of Mathematical Sciences, Indiana University, Purdue University Indianapolis, Indianapolis, IN, 46202, USA
,
V RoytburdDepartment of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA
&
G SivashinskySchool of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel;The Benjamin Levich Institute for Physico-Chemical Hydrodynamics, The City College of New York, New York, NY, 10031, USA
Pages 479-496 | Received 20 Jan 1998, Published online: 19 Aug 2006

Citations (14)

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I Brailovsky, M Frankel & G Sivashinsky. (2000) Galloping and spinning modes of subsonic detonation. Combustion Theory and Modelling 4:1, pages 47-60.
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Articles from other publishers (13)

Jun Yu, Kewang Chen & Laura K. Gross. 2019. Finite Difference Methods. Theory and Applications. Finite Difference Methods. Theory and Applications 646 653 .
Michael Reardon & Jun Yu. (2015) Interaction of Weakly Unstable Auto-Oscillatory Modes in a Solid Propellant Combustion Model. SIAM Journal on Applied Mathematics 75:3, pages 1120-1141.
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I. Brailovsky, M. Frankel, L. Kagan & G. Sivashinsky. (2010) On Oscillatory Instability in Convective Burning of Gas-Permeable Explosives. Mathematical Modelling of Natural Phenomena 6:1, pages 3-16.
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Y. Yang, L. K. Gross & J. Yu. (2010) Comparison Study of Dynamics in One-Sided and Two-Sided Solid-Combustion Models. SIAM Journal on Applied Mathematics 70:8, pages 3022-3038.
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J. H. Park, A. Bayliss & B. J. Matkowsky. (2008) Dynamics in a rod model of solid flame waves revisited. International Journal of Self-Propagating High-Temperature Synthesis 17:1, pages 1-19.
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Dmitry Golovaty. (2007) On Step‐Function Reaction Kinetics Model in the Absence of Material Diffusion. SIAM Journal on Applied Mathematics 67:3, pages 792-809.
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J. H. Park, A. Bayliss, B. J. Matkowsky & A. A. Nepomnyashchy. (2006) On the Route to Extinction in Nonadiabatic Solid Flames. SIAM Journal on Applied Mathematics 66:3, pages 873-895.
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Michael Frankel & Victor Roytburd. (2005) Dynamics of SHS in periodic media. Nonlinear Analysis: Theory, Methods & Applications 63:5-7, pages e1507-e1515.
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Stephen A. Cardarelli, Dmitry Golovaty, L.K. Gross, Vitaliy T. Gyrya & Jianping Zhu. (2005) A numerical study of one-step models of polymerization: Frontal versus bulk mode. Physica D: Nonlinear Phenomena 206:3-4, pages 145-165.
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L. K. Gross & J. Yu. (2005) Weakly Nonlinear and Numerical Analyses of Dynamics in a Solid Combustion Model. SIAM Journal on Applied Mathematics 65:5, pages 1708-1725.
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Michael Frankel & Victor Roytburd. (2004) Frequency locking for combustion synthesis in a periodic medium. Physics Letters A 329:1-2, pages 68-75.
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L. K. Gross. (2002) Weakly Nonlinear Dynamics of Interface Propagation. Studies in Applied Mathematics 108:4, pages 323-350.
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Gregory I. Sivashinsky. (2002) Some developments in premixed combustion modeling. Proceedings of the Combustion Institute 29:2, pages 1737-1761.
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