# Uniqueness of Weak Solutions to a Prion Equation with Polymer Joining

## TL;DR

This paper proves the uniqueness of weak solutions in a mathematical model describing prion proliferation involving polymerization, splitting, and joining, extending previous work on existence of solutions.

## Contribution

It establishes the first proof of uniqueness for weak solutions in a complex prion proliferation model with polymer joining.

## Key findings

- Uniqueness of weak solutions is proven for the prion model.
- The model includes polymerization, splitting, and joining processes.
- Global weak solutions exist for unbounded reaction rates.

## Abstract

We consider a model for prion proliferation that includes prion polymerization, polymer splitting, and polymer joining. The model consists of an ordinary differential equation for the prion monomers and a hyperbolic nonlinear differential equation with integral terms for the prion polymers and was shown to possess global weak solutions for unbounded reaction rates [11]. Here we prove the uniqueness of weak solutions.