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Zbl 1170.80332
Momoniat, E.
A thermal explosion in a cylindrical vessel: a non-classical symmetry approach. (English)
[J] Int. J. Mod. Phys. B 23, No. 14, 3089-3099 (2009). ISSN 0217-9792

Summary: New solutions to the Frank--Kamenetskii partial differential equation modeling a thermal explosion in a cylindrical vessel are obtained. The classical Lie group method is used to determine an approximate solution valid in a small interval around the axis of the cylinder. Non-classical symmetries are used to determine solutions valid after blow-up. These solutions have multiple singularities. Solutions are plotted and analyzed.
MSC 2000:
*80A25 Combustion, interior ballistics

Keywords: blow-up; Lie point symmetries; non-classical symmetries; nonlinear diffusion equation

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