Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere
Abbreviated Journal Title
Appl. Math. Mech.-Engl. Ed.
Lane-Emden equation; bifurcation; thermal explosion; analytical method; DIFFERENTIAL-EQUATIONS; PERTURBATIVE APPROACH; 1ST INTEGRALS; Mathematics, Applied; Mechanics
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.
Applied Mathematics and Mechanics-English Edition
"Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere" (2013). Faculty Bibliography 2010s. 4585.