Approximate Traveling Waves in Linear Reaction-Hyperbolic Equations

Linear reaction‐hyperbolic equations arise in the transport of neurofilaments and membrane‐bound organelles in axons. The profile of the solution was shown by simulations to be approximately that of a traveling wave; this was also suggested by formal calculations [M. C. Reed, S. Venakides, and J. J. Blum, SIAM J. Appl. Math., 50 (1990), pp. 167–180]. In this paper we prove such a result rigorously.

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