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On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere

Published online by Cambridge University Press:  17 February 2009

R. O. Weber ,
G. C. Wake ,
H. S. Sidhu ,
G. N. Mercer ,
B. F. Gray ,
W. Derrick  and
E. Balakrishnan
R. O. Weber
Affiliation:
School of Mathematics and Statistics, University College, University of New South Wales; Australian Defence Force Academy, Canberra 2600, Australia.
G. C. Wake
Affiliation:
Department of Mathematics, University of Canterbury, Christchurch, New Zealand.
H. S. Sidhu
Affiliation:
School of Mathematics and Statistics, University College, University of New South Wales; Australian Defence Force Academy, Canberra 2600, Australia.
G. N. Mercer
Affiliation:
School of Mathematics and Statistics, University College, University of New South Wales; Australian Defence Force Academy, Canberra 2600, Australia.
B. F. Gray
Affiliation:
School of Chemistry, Macquarie University, Sydney, NSW, Australia.
W. Derrick
Affiliation:
Department of Mathematics, University of Montana, Missoula, MT, USA.
E. Balakrishnan
Affiliation:
Department of Mathematics and Statistics, Sultan Qaboos University, Sultanate of Oman.
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Abstract

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Steady state solutions for spontaneous thermal ignition in a unit sphere are considered. The multiplicity of unstable, intermediate, steady state, temperature profiles is calculated and shown for selected parameter values. The crossing of the temperature profiles corresponding to the unstable, intermediate, steady states is exhibited in a particular case and is proven in general using elementary ideas from analysis. Estimates of the location of crossing points are given.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 1 , July 2001 , pp. 77 - 85
Copyright
Copyright © Australian Mathematical Society 2001

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