Travelling waves in the stochastic Nagumo equation

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Ore: 16.00 

Relatrice:

• Carina Geldhauser (Sheffield University)

Abstract:

In this talk we discuss the effect of stochastic perturbations on travelling waves in the Nagumo equation, a bistable reaction-diffusion partial differential equations modelling signal propagation through nerve fibres. The dynamics of this equation depends not only on the noise: spatial discretization can lead to failure of wave propagation already in the deterministic case. We give an overview on existing results and show under which conditions the discrete-stochastic variants of the Nagumo equation have "stable" solutions, in the sense that they stay close, on long time scales, to the classical monotone Nagumo front with high probability. This is joint work with Christian Kuehn (TU Munich).

Referente: Fabio Bagagiolo