Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Threshold behavior and propagation for nonlinear differential-difference systems motivated by modeling myelinated axons

Authors: Jonathan Bell and Chris Cosner
Journal: Quart. Appl. Math. 42 (1984), 1-14
MSC: Primary 92A10; Secondary 34K15
DOI: https://doi.org/10.1090/qam/736501
MathSciNet review: 736501
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Abstract: Using a comparison theorem technique, we study the long time behavior of certain classes of nonlinear difference-differential systems. Zero is a solution for these systems. We are concerned in this paper with conditions forcing nonconvergence to zero of solutions as time approaches infinity; that is, we obtain threshold properties of the systems. The results parallel results by Aronson and Weinberger on reaction-diffusion equations somewhat, and the study was motivated by consideration of models for myelinated nerve axons.

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

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DOI: https://doi.org/10.1090/qam/736501
Article copyright: © Copyright 1984 American Mathematical Society

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