On the existence and uniqueness of solutions of the configurational probability diffusion equation for the generalized rigid dumbbell polymer model
Ionel Sorin Ciuperca, Liviu Iulian Palade · Dynamics of Partial Differential Equations · 2010
Kinetic phase-space theories (see [3]) 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.Contents 1. Introduction 245 2. Evolutionary boundary value problems 246 3. Stationary boundary value problems 257 4. Final comments 262 5.