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Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type

✍ Scribed by Carolus Reinecke; Guido Sweers

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
891 KB
Volume
251
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Systems of elliptic partial differential equations which are coupled in a noncooperative way, such as the FitzHugh–Nagumo type studied in this paper, in general do not satisfy order preserving properties. This not only results in technical complications but also yields a richer solution structure. We prove the existence of multiple nontrivial solutions. In particular we show that there exists a solution with boundary layer type behaviour, and we will give evidence that this autonomous system for a certain range of parameters has a solution with both a boundary and an internal layer. The analysis uses results from bifurcation theory, variational methods, as well as some pointwise a priori estimates. The final section contains some numerically obtained results.

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✍ Xiaoming He; Wenming Zou 📂 Article 📅 2009 🏛 Elsevier Science 🌐 English ⚖ 625 KB

In this paper we prove the existence and multiplicity of solutions for the elliptic system with nonlinear coupling at the smooth boundary given by where Ω is a bounded domain of R N with smooth boundary, ∂/∂ν is the outer normal derivative. The proofs are done under suitable assumptions on the Ham