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
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