On the convergence rate of the nonlinear-hyperbolic systems for axonal transport
Abstract
In this paper, we consider a class of nonlinear reaction-hyperbolic systems with relaxation terms as models for axonal transport in neuroscience. We show the Kruzkov entropy-satisfying BV-solutions of the systems converge towards the solution of an equilibrium model at the rate of in L1 norm as the relaxation time tends to zero. But we don't make sure the rate is optimal.
Keywords
Cite
@article{arxiv.1502.01081,
title = {On the convergence rate of the nonlinear-hyperbolic systems for axonal transport},
author = {Wentao Cao and Feimin Huang},
journal= {arXiv preprint arXiv:1502.01081},
year = {2015}
}
Comments
The paper is being modified by one of the writer Feimin Huang but need some time, since he want it to be more clear in some words and formula, for example Step 2 in the proof of Theroem 2.1. Besides, we want to do more work on the problem, prove the convergence rate $O(\sqrt{\delta})$ is optimal. Thus We will submmit our new manuscript in some time later, therefore, we want to withdraw the paper