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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
