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On the disappearance of criticality in the theory of thermal ignition

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Abstract

A recent article by K. K. Tam in this journal stated results on the values of the activation energy for which a nonlinear eigenvalue problem, which arises in the steady-state theory of thermal ignition, has multiple solutions. This report points to an error contained therein and gives the corrected values of the activation energy for which multiplicity occurs.

Zusammenfassung

Eine vor kurzem erschienene Arbeit in dieser Zeitschrift von K. K. Tam stellte Ergebnisse für die Werte der Aktivierungsenergie fest, für die ein nichtlineares Eigenwert-Problem, das in der stationären Theorie der thermischen Zündung entsteht, vielfache Lösungen hat. Dieser Bericht weist auf einen darin enthaltenen Fehler hin und gibt die korrigierten Werte der Aktivierungsenergie, für die es vielfache Lösungen gibt.

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References

  1. K. K. Tam,On the disappearance of criticality in the theory of thermal ignition. Z. angew. Math. Phys.31, 762 (1980).

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  2. T. Boddington, P. Gray, and G. C. Wake,Criteria for thermal explosions with and without reactant consumption. Proc. Roy. Soc., Ser. A357, 403 (1977).

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  3. N. W. Bazley and G. C. Wake,The disappearance of criticality in the theory of thermal ignition. Z. angew. Math. Phys.29, 971 (1978).

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  4. K. F. Fenaughty, A. A. Lacey, and G. C. Wake,The disappearance of criticality for small activation energy with arbitrary Biot number. Combustion and Flame, in press.

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Authors and Affiliations

  1. Mathematics Dept., Victoria University, Wellington, New Zealand

    A. A. Lacey & G. C. Wake

Authors
  1. A. A. Lacey
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  2. G. C. Wake
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Lacey, A.A., Wake, G.C. On the disappearance of criticality in the theory of thermal ignition. Z. angew. Math. Phys. 33, 406–407 (1982). https://doi.org/10.1007/BF00944448

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  • DOI: https://doi.org/10.1007/BF00944448

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