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

    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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