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Original Articles

Rigorous Bounds and Relations among Spatial and Temporal Approximations in the Theory of Combustion

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Pages 153-162 | Received 16 Jul 1979, Accepted 03 Mar 1980, Published online: 27 Apr 2007

REFERENCES

  • Boddington , T. , Gray , P. , and Wake , G. C. ( 1977 ). Criteria for thermal explosions with and without reactant consumption . Proc. R. Soc. Land ., A. 357 , 403 .
  • Chandra , J. and Davis , P. W. ( 1979 ). Comparison theorems for systems of reaction-diffusion equations , in Lakshmikantham, V. (Ed.) , Applied Nonlinear Analysis . Academic Press , New York .
  • Frank-Kamenetskii , D. A. ( 1945 ). On the mathematical theory of thermal explosions. 11 . Induction period near the explosion limit; correction for the concentration change . Acta Physicochim. URSS , 20 , 729 .
  • Frank-Kamenetskii , D. A. ( 1969 ). Diffusion and Heat Transfer in Chemical Kinetics . John P. Appleton (translation ed,) , Plenum Press , New York .
  • Gray , P. , and Lee , P. R. ( 1967 a). Thermal explosion theory , in Tipper, C. F. H., (Ed.) Oxidation and Combustion Reviews , Vol. 2 . Elsevier , Amsterdam .
  • Gray , P. , and Lee , P. R. ( 1967 b). Studies on criticality temperature profiles in explosive systems and criteria for criticality in thermal explosions . Eleventh Symposium (International) on Combustion , The Combustion Institute , Pittsburgh .
  • Kassoy , D. R. and Linan , A. ( 1978 ). The influence' of reactant consumption on the critical conditions for homogeneous thermal explosions . Q. Jl. Mech. Appl. Malh ., 31 , 99 .
  • Merzhanov , A. G. , and Averson , A. E. ( 1971 ). The present state of the thermal ignition theory an invited review . Combustion and Flame , 16 , 89 .
  • Parks , J. R. ( 1961 ). Criticality criteria for various configurations of a self-heating chemical as functions of activation energy and temperature of assembly . J. Chcm. Phys ., 34 , 46 .
  • Protter , M. H. , and Weinberger , H. ( 1967 ). Maximum Principles in Differential Equations . Prentice-Hall , Englewood Cliffs , New Jersey .
  • Thomas , P. H. ( 1961 ). Effect of reactant consumption on the induction period and critical condition for a thermal explosion . Proc. R. Soc. Land , A . 262 , 192 .
  • Tyler , B. J. , and Wesley , T. A. B. ( 1967 ). Numerical calculations o( the critical conditions in thermal explosion theory with reactant consumption . Eleventh Symposium (International) on Combustion , The Combustion Institute , Pittsburgh .

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