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?)

  • [1] D. G. Aronson and H. F. Weinberger: Nonlinear diffusion in population genetics, combustion, and nerve propagation, Proceedings of the Tulane Program in Partial Differential Equations and Related Topics, Lecture Notes in Math., vol. 446, Springer-Verlag, New York, 1975 MR 0427837
  • [2] J. Bell, Some threshold results for models of myelinated nerves, Math. Biosciences 54 (1981), 181-190 MR 630848
  • [3] H. Cohen, Nonlinear diffusion models, Studies in Applied Mathematics, ed. A. Taub, Math. Assoc. Amer., 1971
  • [4] P. Morell and W. T. Norton, Myelin, Sci. Amer. 242 (1980), 88-118
  • [5] J. Rinzel, Integration and propagation of neuroelectric signals, Studies in Mathematical Biology, ed. S. A. Levin, Math. Assoc. Amer., 1977
  • [6] A. C. Scott, Analysis of a myelinated nerve model, Bull. Math. Biophys. 26 (1964), 247-254
  • [7] W. Walter, Differential and integral inequalities, Springer-Verlag, New York, 1970 MR 0271508

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

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