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

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