On the convergence rate of a class of reaction hyperbolic systems for axonal transport

In this paper, we consider a class of reaction hyperbolic systems for axonal transport arising in neuroscience which can be regarded as hyperbolic systems with relaxation. We prove the BV entropy solutions of the hyperbolic systems converge toward to the unique entropy solution of the equilibrium equation at the optimal rate in L1 norm as the relaxation time δ tends to zero.