2008 | OriginalPaper | Chapter
No Radial Symmetries in the Arrhenius-Semenov Thermal Explosion Equation
Authors : Karl Gustafson, Ed Ash
Published in: Functional Analysis and Evolution Equations
Publisher: Birkhäuser Basel
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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.