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

Authors
Weber, RO Wake, GC Sidhu, HS Mercer, GN Gray, BF Derrick, W Balakrishnan, E
Citation
Ro. Weber et al., On the crossing of intermediate unstable steady state solutions for thermal ignition in a sphere, ANZIAM J, 43, 2001, pp. 77-85
Citations number
20
Categorie Soggetti
Mathematics
Journal title
ANZIAM JOURNAL
ISSN journal
14424436 → ACNP
Volume
43
Year of publication
2001
Part
1
Pages
77 - 85
Database
ISI
SICI code
1442-4436(200107)43:<77:OTCOIU>2.0.ZU;2-7
Abstract
Steady state solutions for spontaneous thermal ignition in a unit sphere ar e considered. The multiplicity of unstable, intermediate, steady state, tem perature profiles is calculated and shown for selected parameter values. Th e crossing of the temperature profiles corresponding to the unstable, inter mediate, steady states is exhibited in a particular case and is proven in g eneral using elementary ideas from analysis. Estimates of the location of c rossing points are given.