Premium
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.