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# Dynamics of Partial Differential Equations

## Volume 7 (2010)

### Number 3

### On the existence and uniqueness of solutions of the configurational probability diffusion equation for the generalized rigid dumbbell polymer model

Pages: 245 – 263

DOI: http://dx.doi.org/10.4310/DPDE.2010.v7.n3.a3

#### Authors

#### Abstract

Kinetic phase-space theories have long been associated with successfully predicting the rheological properties of a variety of macromolecular fluids. Their cornerstone is the configurational probability density, essential to calculating the stress tensor. This function is a solution to the probability diffusion equation. In Section 2 we prove the existence and uniqueness of solutions to the corresponding evolutionary diffusion equation, in Section 3 to the stationary (time independent) equation; these problems, within the context of polymer dynamics theory, did not receive attention until now.

#### Keywords

phase-space kinetic theory, rigid dumbbell chains, Fokker-Planck-Smoluchowski configurational probability equation, existence and uniqueness of solutions

#### 2010 Mathematics Subject Classification

35-xx, 76-xx