Propagation failure  in the discrete Nagumo equation

Hupkes, H.; Pelinovsky, D.; Sandstede, B.

doi:10.1090/S0002-9939-2011-10757-3

Propagation failure in the discrete Nagumo equation
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by H. J. Hupkes, D. Pelinovsky and B. Sandstede PDF

Proc. Amer. Math. Soc. 139 (2011), 3537-3551 Request permission

Abstract:

We address the classical problem of propagation failure for monotonic fronts of the discrete Nagumo equation. For a special class of nonlinearities that support unpinned “translationally invariant” stationary monotonic fronts, we prove that propagation failure cannot occur. Properties of travelling fronts in the discrete Nagumo equation with such special nonlinear functions appear to be similar to those in the continuous Nagumo equation.

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