Some properties of the Doi–Edwards and K-BKZ equations and operators

We prove uniqueness of smooth solutions for a one dimensional K-BKZ equation with degenerated constitutive functions, and state an existence and uniqueness result. Our results apply to the Doi–Edwards micro–macro model in the case of a shear flow and under the independent alignment assumption. We also prove that a K-BKZ related operator is invertible within the previous functional framework.