Diffusion dependence of the FitzHugh-Nagumo equations
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- by Clyde Collins
- Trans. Amer. Math. Soc. 280 (1983), 833-839
- DOI: https://doi.org/10.1090/S0002-9947-1983-0716853-8
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Abstract:
We investigate the behavior of the solutions of \[ \begin {array}{*{20}{c}} {{u_t} = {u_{x x}} - \alpha u - v + f(u),} \\ {{v_t} = \eta {v_{x x}} + \sigma u - \gamma v,} \\ \end {array} \] as $\eta$ tends to zero from above.References
- C. Collins, Length dependence of solutions of generalized FitzHugh-Nagumo equations, Ph.D. Thesis, Indiana Univ., Bloomington, 1981.
- Clyde Collins, Length dependence of solutions of FitzHugh-Nagumo equations, Trans. Amer. Math. Soc. 280 (1983), no. 2, 809–832. MR 716852, DOI 10.1090/S0002-9947-1983-0716852-6
- Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244 T. Kato, Perturbation theory for linear operators, Springer-Velag, New York, 1980.
- Jeffrey Rauch and Joel Smoller, Qualitative theory of the FitzHugh-Nagumo equations, Advances in Math. 27 (1978), no. 1, 12–44. MR 487094, DOI 10.1016/0001-8708(78)90075-0 M. Schonbek, Technical reports 1739 and 1740, MRC, Madison, Wisconsin, 1977.
Bibliographic Information
- © Copyright 1983 American Mathematical Society
- 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