Dynamics of Partial Differential Equations

Volume 20 (2023)

Number 2

Polymer kinetic theory temperature dependent configurational probability diffusion equations: Existence of positive solution results

Pages: 135 – 152

DOI: https://dx.doi.org/10.4310/DPDE.2023.v20.n2.a3

Authors

Ionel Sorin Ciuperca (Université Lyon 1, CNRS, Institut Camille Jordan, Villeurbanne, France)

Liviu Iulian Palade (INSA-Lyon, CNRS, Institut Camille Jordan UMR & Pôle de Mathématiques, Villeurbanne, France)

Abstract

A new configurational probability diffusion—CPD—equation that accounts for temperature dependent molecular dynamics for incompressible polymer fluids is introduced. We prove the existence of positive solutions for the corresponding variational formulation using Schauder’s fixed point theory. The polymer fluid macromolecules are modeled as Finitely Extensible Nonlinear Elastic dumbbells, also known as FENE chains.

Keywords

FENE polymer chain models, non-isothermal polymer kintetic theory, dimensionless configurational probability diffusion equation, positive solutions existence results

2010 Mathematics Subject Classification

Primary 35Q35. Secondary 35A15.

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Received 2 December 2022

Published 17 May 2023