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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Diffusion dependence of the FitzHugh-Nagumo equations


Author: Clyde Collins
Journal: Trans. Amer. Math. Soc. 280 (1983), 833-839
MSC: Primary 35K57; Secondary 35B99, 92A09
DOI: https://doi.org/10.1090/S0002-9947-1983-0716853-8
MathSciNet review: 716853
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Abstract: We investigate the behavior of the solutions of

\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} = {u_{x\,x}} - \alpha \,u - v ... ...} = \eta \,{v_{x\,x}} + \sigma \,u - \gamma v,} \\ \end{array} \end{displaymath}

as $ \eta $ tends to zero from above.

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

  • [1] C. Collins, Length dependence of solutions of generalized FitzHugh-Nagumo equations, Ph.D. Thesis, Indiana Univ., Bloomington, 1981.
  • [2] -, Length dependence of solutions of FitzHugh-Nagumo equations, Trans. Amer. Math. Soc. 280 (1983), 809-832. MR 716852 (85d:35059a)
  • [3] D. Henry, Geometric theory of semilinear parabolic equations, Springer-Verlag, New York, 1981. MR 610244 (83j:35084)
  • [4] T. Kato, Perturbation theory for linear operators, Springer-Velag, New York, 1980.
  • [5] J. Rauch and J. Smoller, Qualitative theory of the FitzHugh-Nagumo equations, Adv. in Math. 27 (1978), 12-44. MR 0487094 (58:6759)
  • [6] M. Schonbek, Technical reports 1739 and 1740, MRC, Madison, Wisconsin, 1977.

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DOI: https://doi.org/10.1090/S0002-9947-1983-0716853-8
Article copyright: © Copyright 1983 American Mathematical Society

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