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

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 $O(\sqrt{\delta})$ in L1 norm as the relaxation time $\delta$ tends to zero. But we don't make sure the rate is optimal.