Dynamics of Partial Differential Equations
Volume 7 (2010)
On the existence and uniqueness of solutions of the configurational probability diffusion equation for the generalized rigid dumbbell polymer model
Pages: 245 – 263
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.
phase-space kinetic theory, rigid dumbbell chains, Fokker-Planck-Smoluchowski configurational probability equation, existence and uniqueness of solutions
2010 Mathematics Subject Classification