Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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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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  • [2] Jonathan Bell, Some threshold results for models of myelinated nerves, Math. Biosci. 54 (1981), no. 3-4, 181–190. MR 630848, https://doi.org/10.1016/0025-5564(81)90085-7
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Additional Information

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


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