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
Copyright Status
Unknown
Socpus ID
84891025669 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84891025669
STARS Citation
Reger, K. and Van Gorder, R. A., "Lane-Emden Equations Of Second Kind Modelling Thermal Explosion In Infinite Cylinder And Sphere" (2013). Scopus Export 2010-2014. 5748.
https://stars.library.ucf.edu/scopus2010/5748