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Transactions of the American Mathematical Society

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Length dependence of solutions of FitzHugh-Nagumo equations


Author: Clyde Collins
Journal: Trans. Amer. Math. Soc. 280 (1983), 809-832
MSC: Primary 35K57; Secondary 35B99, 92A09
DOI: https://doi.org/10.1090/S0002-9947-1983-0716852-6
MathSciNet review: 716852
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate the behavior of the solutions of the problem

\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} = {u_{xx}} - \alpha u - \upsil... ... h(t),} & {{u_x}(L,t) = {\upsilon _x}(L,t) = 0} \\ \end{array} \end{displaymath}

where $ t \geqslant 0$ and $ 0 < x < L \leqslant \infty $.

Solutions of the above equations are considered a qualitative model of conduction of nerve axon impulses. Using explicit constructions and semigroup methods, we obtain decay results on the norms of differences between the solution for $ L$ infinite and the solutions when $ L$ is large but finite. We conclude that nerve impulses for long finite nerves become uniformly close to those of the semi-infinite nerves away from the right endpoint of the finite nerve.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0716852-6
Article copyright: © Copyright 1983 American Mathematical Society

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