Asymptotic Behavior of the Solution of the Distribution Diffusion Equation for FENE Dumbbell Polymer Model

Abstract

Abstract. This paper deals with the evolution Fokker-Planck-Smoluchowski configurational probability diffusion equation for the FENE dumbbell model in dilute polymer solutions. We prove the exponential convergence in time of the solution of this equation to a corresponding steady-state solution, for arbitrary velocity gradients.

Existence and uniqueness results for the Doi–Edwards polymer melt model: the case of the (full) nonlinear configurational probability density equation

“…This work is a continuation of that of [3,[5][6][7], where related probability diffusion PDEs of relevance to polymer physics (and rheology) in general have been studied; for other or related types of Fokker-Planck-Smoluchowski PDEs see for example [4,11].…”

On the IAA version of the Doi–Edwards model versus the K-BKZ rheological model for polymer fluids: A global existence result for shear flows with small initial data

“…[1], [2], [4], [5], [7], [11], [14], [15], [16], [17], [21], [25], [27], [28], [31], [33]. However, this activity success hinges on users ability to cope with significant mathematical difficulties.…”