On coupled Lane-Emden equations arising in dusty fluid models

Abstract

We investigate the existence of solutions for mixed boundary value problems in coupled Lane-Emden equations. Such problems arise e.g. in the study of multicomponent diffusion and reaction processes inside catalyst particles under spherical symmetry. In contrast to the frequently applied decomposition method of Adomian, we employ the geometric theory of ODEs to show that this boundary value problem can be transformed into a terminal value problem. To this end, we determine the integral manifold on which solutions of the boundary value problem necessarily lie. This will be done in suitable warped and blown-up coordinates. Moreover, we comment on the numerical implementation.