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Time averaging in turbulence settings may reveal an infinite hierarchy of length scales
On the stability of high Lewis number combustion fronts
1. | Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States, United States |
[1] |
Zhen-Hui Bu, Zhi-Cheng Wang. Stability of pyramidal traveling fronts in the degenerate monostable and combustion equations Ⅰ. Discrete and Continuous Dynamical Systems, 2017, 37 (5) : 2395-2430. doi: 10.3934/dcds.2017104 |
[2] |
Luca Dieci, Cinzia Elia. Smooth to discontinuous systems: A geometric and numerical method for slow-fast dynamics. Discrete and Continuous Dynamical Systems - B, 2018, 23 (7) : 2935-2950. doi: 10.3934/dcdsb.2018112 |
[3] |
Debora Amadori, Wen Shen. Front tracking approximations for slow erosion. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 1481-1502. doi: 10.3934/dcds.2012.32.1481 |
[4] |
Kota Ikeda, Masayasu Mimura. Traveling wave solutions of a 3-component reaction-diffusion model in smoldering combustion. Communications on Pure and Applied Analysis, 2012, 11 (1) : 275-305. doi: 10.3934/cpaa.2012.11.275 |
[5] |
Zhen-Hui Bu, Zhi-Cheng Wang. Global stability of V-shaped traveling fronts in combustion and degenerate monostable equations. Discrete and Continuous Dynamical Systems, 2018, 38 (5) : 2251-2286. doi: 10.3934/dcds.2018093 |
[6] |
Denghui Wu, Zhen-Hui Bu. Multidimensional stability of pyramidal traveling fronts in degenerate Fisher-KPP monostable and combustion equations. Electronic Research Archive, 2021, 29 (6) : 3721-3740. doi: 10.3934/era.2021058 |
[7] |
Andrea Giorgini. On the Swift-Hohenberg equation with slow and fast dynamics: well-posedness and long-time behavior. Communications on Pure and Applied Analysis, 2016, 15 (1) : 219-241. doi: 10.3934/cpaa.2016.15.219 |
[8] |
Chunhua Shan. Slow-fast dynamics and nonlinear oscillations in transmission of mosquito-borne diseases. Discrete and Continuous Dynamical Systems - B, 2022, 27 (3) : 1447-1469. doi: 10.3934/dcdsb.2021097 |
[9] |
Anatoly Neishtadt, Carles Simó, Dmitry Treschev, Alexei Vasiliev. Periodic orbits and stability islands in chaotic seas created by separatrix crossings in slow-fast systems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (2&3, September) : 621-650. doi: 10.3934/dcdsb.2008.10.621 |
[10] |
Claude-Michel Brauner, Josephus Hulshof, Luca Lorenzi, Gregory I. Sivashinsky. A fully nonlinear equation for the flame front in a quasi-steady combustion model. Discrete and Continuous Dynamical Systems, 2010, 27 (4) : 1415-1446. doi: 10.3934/dcds.2010.27.1415 |
[11] |
Jong-Shenq Guo, Ken-Ichi Nakamura, Toshiko Ogiwara, Chang-Hong Wu. The sign of traveling wave speed in bistable dynamics. Discrete and Continuous Dynamical Systems, 2020, 40 (6) : 3451-3466. doi: 10.3934/dcds.2020047 |
[12] |
Paul Carter, Alan R. Champneys. Wiggly canards: Growth of traveling wave trains through a family of fast-subsystem foci. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022036 |
[13] |
C. Connell Mccluskey. Lyapunov functions for tuberculosis models with fast and slow progression. Mathematical Biosciences & Engineering, 2006, 3 (4) : 603-614. doi: 10.3934/mbe.2006.3.603 |
[14] |
Luca Biasco, Laura Di Gregorio. Periodic solutions of Birkhoff-Lewis type for the nonlinear wave equation. Conference Publications, 2007, 2007 (Special) : 102-109. doi: 10.3934/proc.2007.2007.102 |
[15] |
Faustino Sánchez-Garduño, Philip K. Maini, Judith Pérez-Velázquez. A non-linear degenerate equation for direct aggregation and traveling wave dynamics. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 455-487. doi: 10.3934/dcdsb.2010.13.455 |
[16] |
Lianzhang Bao, Zhengfang Zhou. Traveling wave in backward and forward parabolic equations from population dynamics. Discrete and Continuous Dynamical Systems - B, 2014, 19 (6) : 1507-1522. doi: 10.3934/dcdsb.2014.19.1507 |
[17] |
Cunming Liu, Jianli Liu. Stability of traveling wave solutions to Cauchy problem of diagnolizable quasilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4735-4749. doi: 10.3934/dcds.2014.34.4735 |
[18] |
Jonathan E. Rubin. A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium. Discrete and Continuous Dynamical Systems, 2004, 10 (4) : 925-940. doi: 10.3934/dcds.2004.10.925 |
[19] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[20] |
Yuri Latushkin, Roland Schnaubelt, Xinyao Yang. Stable foliations near a traveling front for reaction diffusion systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (8) : 3145-3165. doi: 10.3934/dcdsb.2017168 |
2020 Impact Factor: 1.392
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