ISSN:
1572-9222
Keywords:
Free boundary problems
;
gasless combustion
;
stability
;
Hopf bifurcation
;
35R35
;
35B40
;
80A25
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we analyze a simple free boundary model associated with solid combustion and some phase transition processes. There is strong evidence that this “one-phase” model captures all major features of dynamical behavior of more realistic (and complicated) combustion and phase transition models. The principal results concern the dynamical behavior of the model as a bifurcation parameter (which is related to the activation energy in the case of combustion) varies. We prove that the basic uniform front propagation is asymptotically stable against perturbations for the bifurcation parameter above the instability threshold and that a Hopf bifurcation takes place at the threshold value. Results of numerical simulations are presented which confirm that both supercritical and subcritical Hofp bifurcation may occur for physically reasonable nonlinear kinetic functions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02218858
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