Abstract
The FitzHugh–Nagumo system, composed of a semilinear parabolic equation coupled to a linear ordinary equation, captures the qualitative dynamics of an excitable fibre. The semilinear term encodes the fibre's nonlinear membrane conductance that underlies its excitability. We here establish conditions under which a semilinear term exists that corresponds to specified Neumann data at each end and Dirichlet data at one end.
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