Title

Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere

Authors

Authors

K. Reger;R. A. Van Gorder

Comments

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Abbreviated Journal Title

Appl. Math. Mech.-Engl. Ed.

Keywords

Lane-Emden equation; bifurcation; thermal explosion; analytical method; DIFFERENTIAL-EQUATIONS; PERTURBATIVE APPROACH; 1ST INTEGRALS; Mathematics, Applied; Mechanics

Abstract

We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series (which work well for weak nonlinearity) and the delta-expansion method (valid for strong nonlinearity). From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.

Journal Title

Applied Mathematics and Mechanics-English Edition

Volume

34

Issue/Number

12

Publication Date

1-1-2013

Document Type

Article

Language

English

First Page

1439

Last Page

1452

WOS Identifier

WOS:000328204500002

ISSN

0253-4827

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