Standing pulse solutions for the FitzHugh-Nagumo equations

By Y. Oshita, and I. Ohnishi,

Japan Journal of Industrial and Applied Mathematics volume 20, Article number: 101 (2003)

The abstract is the following:

We are basically concerned with existence of standing pulse solutions for an elliptic equation with a nonlocal term. The problem comes from an activator-inhibitor system such as the FitzHugh-Nagumo equations with inhibitor’s diffusion or arises in the Allen-Cahn equation with the nonlocal term. We prove it mathematically rigorously in a bounded domainΩ ⊂R n (n ≥ 2) with smooth boundary, by employing the Lyapunov-Schmidt reduction method, which is the same kind of way as used typically in [2], [9], [10], [13], for instance.

Standing pulse solutions for the FitzHugh-Nagumo equations

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