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- W1968804557 abstract "This paper is concerned with the study of the FitzHugh-Nagumo equations. These equations arise in mathematical biology as a model of the transmission of electrical impulses through a nerve axon; they are a simplified version of the Hodgkin-Huxley equations. The FitzHugh-Nagumo equations consist of a non-linear diffusion equation coupled to an ordinary differential equation. v t = v xx + f ( v ) − u , u t = σv − γu . We study these equations with either Dirichlet or Neumann boundary conditions, proving local and global existence, and uniqueness of the solutions. Furthermore, we obtain L ∞ estimates for the solutions in terms of the L 1 norm of the boundary data, when the boundary data vanish after a finite time and the initial data are zero. These estimates allow us to prove exponential decay of the solutions." @default.
- W1968804557 created "2016-06-24" @default.
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- W1968804557 date "1978-10-01" @default.
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- W1968804557 title "Boundary value problems for the Fitzhugh-Nagumo equations" @default.
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- W1968804557 doi "https://doi.org/10.1016/0022-0396(78)90027-x" @default.
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