Critical initial conditions for thermal ignition

B. F. Gray*, G. C. Wake

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)


In the conductive theory of thermal ignition, there is a practically important region of parameter space where the heat conduction partial differential equation with a nonlinear (Arrhenius) heat generation term displays two attractors. Their basins of attraction (particularly that of the minimal solutions) are of great practical importance. Good estimates for the latter region are obtained by a method of spatial averaging of the nonlinear term which give very small errors for large classes of initial conditions, provided the latter are not too 'spikey'. For 'hot spot' type initial conditions the method still works and gives satisfactory estimates. The bound is focussed on the critical initial energy.

Original languageEnglish
Pages (from-to)65-75
Number of pages11
JournalMathematical and Computer Modelling
Issue number8
Publication statusPublished - 1993
Externally publishedYes


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