No Radial Symmetries in the Arrhenius-Semenov Thermal Explosion Equation

Karl Gustafson () and Ed Ash
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Karl Gustafson: University of Colorado at Boulder, Department of Mathematics
Ed Ash: University of Colorado at Boulder, Department of Mathematics

A chapter in Functional Analysis and Evolution Equations, 2007, pp 357-370 from Springer

Abstract: Abstract Nonlinear evolution equations in the theory of exothermic chemical reactions lead to semilinear parabolic and elliptic boundary value problems with exponential nonlinearities. In contrast to a commonly employed (Frank-Kamenetskii) approximation, which permits similarity variables for the asymptotic analysis of solution behavior near thermal runaway, we show that the more correct (Arrhenius-Semenov) equation permits no radial symmetries. We also establish that a more general class of thermal nonlinearities also possess no symmetries.

Keywords: Nonlinear evolution equations; Bifurcation; Symmetries; Arrhenius-Semenov equation; explosion criticality (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7643-7794-6_23

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DOI: 10.1007/978-3-7643-7794-6_23

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