American Institute of Mathematical Sciences

Advanced
2005, 2005(Special): 287-296. doi: 10.3934/proc.2005.2005.287

Dynamical structure of one-phase model of solid combustion

Michael L. Frankel 1, and  Victor Roytburd 2,

1. 

Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216, United States
2. 

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590

Received  September 2004 Revised  April 2005 Published  September 2005

We present results of a numerical study of complex dynamics generated by a one-phase free-boundary problem with kinetics modeling gasless combustion. We study dynamical structure generated by the problem using bifurcational diagrams obtained through the correlation dimension. In the case of periodically varying initial concentration the problem exhibits frequency locking. We also demonstrate that a finite-dimensional reduction via a method of collocations leads to a similar dynamical structure.
Keywords: Free boundary, bifurcation diagram., correlation dimension, frequency locking.
Mathematics Subject Classification: 58F15, 58F17; Secondary: 53C3.
Citation: Michael L. Frankel, Victor Roytburd. Dynamical structure of one-phase model of solid combustion. Conference Publications, 2005, 2005 (Special) : 287-296. doi: 10.3934/proc.2005.2005.287
[1]

Lutz Recke, Anatoly Samoilenko, Alexey Teplinsky, Viktor Tkachenko, Serhiy Yanchuk. Frequency locking of modulated waves. Discrete & Continuous Dynamical Systems - A, 2011, 31 (3) : 847-875. doi: 10.3934/dcds.2011.31.847
[2]

Satoshi Kosugi, Yoshihisa Morita, Shoji Yotsutani. A complete bifurcation diagram of the Ginzburg-Landau equation with periodic boundary conditions. Communications on Pure & Applied Analysis, 2005, 4 (3) : 665-682. doi: 10.3934/cpaa.2005.4.665
[3]

Rafael Labarca, Solange Aranzubia. A formula for the boundary of chaos in the lexicographical scenario and applications to the bifurcation diagram of the standard two parameter family of quadratic increasing-increasing Lorenz maps. Discrete & Continuous Dynamical Systems - A, 2018, 38 (4) : 1745-1776. doi: 10.3934/dcds.2018072
[4]

Yaodan Huang, Zhengce Zhang, Bei Hu. Bifurcation from stability to instability for a free boundary tumor model with angiogenesis. Discrete & Continuous Dynamical Systems - A, 2019, 39 (5) : 2473-2510. doi: 10.3934/dcds.2019105
[5]

Junde Wu. Bifurcation for a free boundary problem modeling the growth of necrotic multilayered tumors. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3399-3411. doi: 10.3934/dcds.2019140
[6]

Zhangxin Chen, Qiaoyuan Jiang, Yanli Cui. Locking-free nonconforming finite elements for planar linear elasticity. Conference Publications, 2005, 2005 (Special) : 181-189. doi: 10.3934/proc.2005.2005.181
[7]

Ruishu Wang, Lin Mu, Xiu Ye. A locking free Reissner-Mindlin element with weak Galerkin rotations. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 351-361. doi: 10.3934/dcdsb.2018086
[8]

Aixian Zhang, Zhengchun Zhou, Keqin Feng. A lower bound on the average Hamming correlation of frequency-hopping sequence sets. Advances in Mathematics of Communications, 2015, 9 (1) : 55-62. doi: 10.3934/amc.2015.9.55
[9]

Xing Liu, Daiyuan Peng. Frequency hopping sequences with optimal aperiodic Hamming correlation by interleaving techniques. Advances in Mathematics of Communications, 2017, 11 (1) : 151-159. doi: 10.3934/amc.2017009
[10]

Freddy Dumortier, Robert Roussarie. Bifurcation of relaxation oscillations in dimension two. Discrete & Continuous Dynamical Systems - A, 2007, 19 (4) : 631-674. doi: 10.3934/dcds.2007.19.631
[11]

Xing Liu, Daiyuan Peng. Sets of frequency hopping sequences under aperiodic Hamming correlation: Upper bound and optimal constructions. Advances in Mathematics of Communications, 2014, 8 (3) : 359-373. doi: 10.3934/amc.2014.8.359
[12]

Limengnan Zhou, Daiyuan Peng, Hongyu Han, Hongbin Liang, Zheng Ma. Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation. Advances in Mathematics of Communications, 2018, 12 (1) : 67-79. doi: 10.3934/amc.2018004
[13]

Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden. Minimum free energy in the frequency domain for a heat conductor with memory. Discrete & Continuous Dynamical Systems - B, 2010, 14 (3) : 793-816. doi: 10.3934/dcdsb.2010.14.793
[14]

Jean-François Rault. A bifurcation for a generalized Burgers' equation in dimension one. Discrete & Continuous Dynamical Systems - S, 2012, 5 (3) : 683-706. doi: 10.3934/dcdss.2012.5.683
[15]

Hayk Mikayelyan, Henrik Shahgholian. Convexity of the free boundary for an exterior free boundary problem involving the perimeter. Communications on Pure & Applied Analysis, 2013, 12 (3) : 1431-1443. doi: 10.3934/cpaa.2013.12.1431
[16]

Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10
[17]

Avner Friedman. Free boundary problems arising in biology. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 193-202. doi: 10.3934/dcdsb.2018013
[18]

Todd Young. Partially hyperbolic sets from a co-dimension one bifurcation. Discrete & Continuous Dynamical Systems - A, 1995, 1 (2) : 253-275. doi: 10.3934/dcds.1995.1.253
[19]

Xinfu Chen, Huibin Cheng. Regularity of the free boundary for the American put option. Discrete & Continuous Dynamical Systems - B, 2012, 17 (6) : 1751-1759. doi: 10.3934/dcdsb.2012.17.1751
[20]

Xiaoshan Chen, Fahuai Yi. Free boundary problem of Barenblatt equation in stochastic control. Discrete & Continuous Dynamical Systems - B, 2016, 21 (5) : 1421-1434. doi: 10.3934/dcdsb.2016003

 Impact Factor: 

Tools

Metrics

  • PDF downloads (10)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences