Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/553
 Title: Standing Waves in the FitzHugh-Nagumo System and a Problem in Combinatorial Geometry Authors: Winter, MWei, J Keywords: FitzHugh-Nagumo system;Localised energy method;Standing waves;Optimal configuration Issue Date: 2006 Publisher: Springer Citation: Math Z 254: 359-383, 2006 Abstract: We show that there is a close relation between standing-wave solutions for the FitzHugh-Nagumo system $\Delta u +u(u-a)(1-u) - \delta v=0, \ \ \Delta v-\delta \gamma v + u=0 \ \ \mbox{in} \ R^N,$ $u, v \to 0 \ \mbox{as} \ |x| \to +\infty$ where $00$ such that for $0<\delta <\delta_K$, there exists a standing-wave solution $(u_{\delta},v_{\delta})$ to the FitzHugh-Nagumo system with the property that $u_{\delta}$ has $K$ spikes $Q_{1}^\delta, ..., Q_K^\delta$ and $(\frac{1}{l^\delta} Q_1^\delta, ..., \frac{1}{l^\delta} Q_K^\delta)$ approaches an optimal configuration in (*), where $l^\delta=\min_{i \not = j} |Q_i^\delta -Q_j^\delta| = \frac{1}{ \sqrt{a} -\beta} \log \frac{1}{\delta} ( 1+o(1))$. URI: http://bura.brunel.ac.uk/handle/2438/553 DOI: http://doi.dx.org/10.1007/s00209-006-0952-8 Appears in Collections: Dept of Mathematics Research PapersMathematical Sciences

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