Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport

TL;DR

This paper establishes the global existence of entropy solutions for nonlinear reaction-hyperbolic systems modeling axonal transport, and justifies the limit where biochemical processes are faster than transport.

Contribution

It introduces a rigorous method to prove the existence of entropy solutions and analyzes the limiting behavior as biochemical reactions accelerate.

Findings

Proved global existence of entropy BV-solutions.

Justified the limit of fast biochemical processes.

Applied hyperbolic methods to biological transport models.

Abstract

This paper is concerned with a class of nonlinear reaction-hyperbolic systems as models for axonal transport in neuroscience. We show the global existence of entropy-satisfying BV-solutions to the initial-value problems by using hyperbolic-type methods. Moreover, we rigorously justify the limit as the biochemical processes are much faster than the transport ones.