English

On the convergence rate of the nonlinear-hyperbolic systems for axonal transport

Analysis of PDEs 2015-03-06 v3

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 O(δ)O(\sqrt{\delta}) in L1 norm as the relaxation time δ\delta 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