A turning point asymptotic expansion for a rigid-dumbbell polymer fluid probability configurational equation for fast shear flows

Article type: Research Article

Authors: Ciuperca, Ionel Sorin^{a; b} | Palade, Liviu Iulian^{a; c; *}

Affiliations: [a] Université de Lyon, CNRS, Institut Camille Jordan UMR 5208, France | [b] Université Lyon 1, Bât Braconnier, 43 Boulevard du 11 Novembre 1918, F-69622, Villeurbanne, France. E-mail: ciuperca@math.univ-lyon.fr | [c] INSA-Lyon, Pôle de Mathématiques, Bât. Leonard de Vinci No. 401, 21 Avenue Jean Capelle, F-69621, Villeurbanne, France. E-mail: liviu-iulian.palade@insa-lyon.fr

Correspondence: [*] Corresponding author. Fax: +33 472438529; E-mail: liviu-iulian.palade@insa-lyon.fr.

Abstract: This paper establishes an asymptotic expansion for a second order differential equation with a small diffusion coefficient, which generalizes the configurational probability diffusion equation of the Rigid Dumbbell Model (RDM) of diluted polymer solutions theory for fast shear flows. This is a singular perturbation problem with turning point.

Keywords: Turning point asymptotic problem, rigid dumbbell polymer chain model, fast shear flows, configurational probability diffusion equation

DOI: 10.3233/ASY-171435

Journal: Asymptotic Analysis, vol. 105, no. 1-2, pp. 45-76, 2017