Article Contents
Article Contents

# Asymptotic effects of boundary perturbations in excitable systems

• A Neumann problem in the strip for the Fitzhugh Nagumo system is considered. The transformation in a non linear integral equation permits to deduce a priori estimates for the solution. A complete asymptotic analysis shows that for large $t$ the effects of the initial data vanish while the effects of boundary disturbances $\varphi_1 (t),$ $\varphi_2(t)$ depend on the properties of the data. When $\varphi_1,\,\, \varphi_2$ are convergent for large $t$, the solution is everywhere bounded and depends on the asymptotic values of $\varphi_1 ,$ $\varphi_2$. More, when $\varphi_i \in L^1 (0,\infty) (i=1,2)$ too, the effects are vanishing.
Mathematics Subject Classification: 44A10, 35K57, 35A08.

 Citation:

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