Existence and uniqueness of a density probability solution for the stationary Doi-Edwards equation

TL;DR

This paper establishes the existence, uniqueness, and non-negativity of solutions for a nonlinear stationary Doi-Edwards equation, using perturbation and convergence methods to analyze the equation's solutions.

Contribution

It provides the first rigorous proof of existence and uniqueness for solutions to the stationary Doi-Edwards equation, advancing understanding of this nonlinear model.

Findings

Existence of solutions proved via perturbation argument

Uniqueness established through convergence of evolutionary solutions

Solutions are shown to be non-negative

Abstract

We prove the existence, uniqueness and non negativity of solutions for a nonlinear stationary Doi-Edwards equation. The existence is proved by a perturbation argument. We get the uniqueness and the non negativity by showing the convergence in time of the solution of the evolutionary Doi-Edwards equation towards any stationary solution.