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

Reinecke Carolus | Zendy; Sweers Guido | Zendy

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

Author(s) -

Reinecke Carolus,

Sweers Guido

Publication year - 2003

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200310031

Subject(s) - mathematics , pointwise , type (biology) , a priori and a posteriori , bifurcation , boundary (topology) , mathematical analysis , jump , boundary layer , partial differential equation , range (aeronautics) , nonlinear system , philosophy , ecology , physics , materials science , epistemology , quantum mechanics , composite material , biology , thermodynamics

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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