ANZIAM J.
45 (2003), 35-48
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Sequential eigenfunction expansion for a problem in combustion theory
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M. Al-Refai
Department of Mathematics and Statistics
McGill University
Burnside Hall, Room 1005
805 Sherbrooke St. West
Monterals, Quebec H3A 2K5
Canada
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K. K. Tam
Department of Mathematics and Statistics
McGill University
Burnside Hall, Room 1005
805 Sherbrooke St. West
Monterals, Quebec H3A 2K5
Canada
tam@math.mcgill.ca
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Abstract
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A method of sequential eigenfunction expansion
is developed for a semi-linear parabolic
equation. It allows the time-dependent
coefficients of the eigenfunctions to be
determined sequentially and iterated to reach
convergence. At any stage, only a single ordinary
differential equation needs to be considered, in
contrast to the Galerkin method which requires
the consideration of a system of equations. The
method is applied to a central problem in
combustion theory to provide a definitive answer
to the question of the influence of the initial
data in determining whether the solution is sub-
or super-critical, in the case of multiple
steady-state solutions. It is expected this
method will prove useful in dealing with similar
problems.
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