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Zbl 0739.34060
Zinner, B.
Stability of traveling wavefronts for the discrete Nagumo equation.
(English)
[J] SIAM J. Math. Anal. 22, No.4, 1016-1020 (1991). ISSN 0036-1410; ISSN 1095-7154/e

Author's abstract: It has been shown that the discrete Nagumo equation $\dot u\sb n=d(u\sb{n-1}-2u\sb n+u\sb{n+1})+f(u\sb n)$, $n\in\bbfZ$, has a traveling wavefront solution for sufficiently strong coupling $d$. In this paper it is shown that such a traveling wavefront is unique (up to a shift in time) and globally stable.''.
[P.Poláčik (Bratislava)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
35K57 Reaction-diffusion equations
34A35 ODE of infinite order

Keywords: lower solution technique; myelinated axon; discrete cells; stability; discrete Nagumo equation; traveling wavefront solution

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