Effect on Pushed Fronts

We consider first an example of a pushed front propagating into an unstable state, namely Ben-Jacob s case with a cutoff, F(p) = 0 p - e)p(l - p)(l + ap). A pushed front occurs for a 2 and Vq = ( /a + see (4.14). In this 

We consider next a front propagating into a metastable state for the Nagumo equation, F p) = 6 p - e)/o(l - p) p - a). The front velocity in the absence of a cutoff is vq = l/ /2 - a /l. Equation (4.86) yields v Exact analytical results for the front solutions can be obtained if the reaction term F(p) with a cutoff is replaced by a piecewise linear approximation. The dependence of the velocity shift on the cutoff displays good agreement with the results by Brunet and Derrida and Kessler et al. [495]. 

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