Dynamical structure of one-phase model of solid combustion

Pages: 287 - 296, Issue Special, August 2005

 Abstract        Full Text (374.3K)              

Michael L. Frankel - Department of Mathematical Sciences, Indiana University – Purdue University Indianapolis, Indianapolis, IN 46202-3216, United States (email)
Victor Roytburd - Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, United States (email)

Abstract: 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, correlation dimension, frequency locking, bifurcation diagram.
Mathematics Subject Classification:  58F15, 58F17; Secondary: 53C35.

Received: September 2004;      Revised: April 2005;      Published: September 2005.