Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type
Solutions with internal jump for an autonomous elliptic system of FitzHugh–Nagumo type
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FitzHugh-Nagumo 型自治椭圆系统的内部跳跃解
DOI：
10.1002/mana.200310031
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发表时间：
2003
影响因子：
1
通讯作者：
G. Sweers
中科院分区：
文献类型：
--
作者：
C. Reinecke;G. Sweers
非合作耦合的椭圆型偏微分方程系统，如本文所研究的FitzHugh-Nagumo型，一般不满足保序性质。这不仅会导致技术复杂化，而且会产生更丰富的解决方案结构。我们证明了多个非平凡解的存在性。特别是，我们表明，存在一个解决方案与边界层型行为，我们将给出证据，这个自治系统的参数在一定范围内有一个解决方案的边界和内部层。分析使用分歧理论，变分方法，以及一些逐点的先验估计的结果。最后一节包含一些数值计算得到的结果。
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.