Title

Lane-Emden Equations Of Second Kind Modelling Thermal Explosion In Infinite Cylinder And Sphere

Keywords

analytical method; bifurcation; Lane-Emden equation; thermal explosion

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 δ-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. © 2013 Shanghai University and Springer-Verlag Berlin Heidelberg.

Publication Date

12-1-2013

Publication Title

Applied Mathematics and Mechanics (English Edition)

Volume

34

Issue

12

Number of Pages

1439-1452

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s10483-013-1758-6

Socpus ID

84891025669 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84891025669

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