Existence of traveling wavefront solutions for the discrete Nagumo equation
Existence of traveling wavefront solutions for the discrete Nagumo equation
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DOI：
10.1016/0022-0396(92)90142-a
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发表时间：
1992-03
影响因子：
2.4
通讯作者：
B. Zinner
中科院分区：
文献类型：
--
作者：
B. Zinner
本文证明了离散Nagumo方程n= d（un − 1+ 2un + n+ 1）+ f（un），n ε Z在充分强耦合d下存在行波解.首先将该问题简化为不动点问题，并利用布劳威尔不动点定理求解。简化问题的解决方案，然后继续通过指数理论的近似问题的解决方案。在最后一步中，证明了近似问题的解有一个极限点，该极限点对应于原问题的解。
In this paper we show that the discrete Nagumo equation n= d (u n− 1+ 2u n+ n+ 1)+ f (u n), n ε Z has a traveling wave solution for sufficiently strong coupling d. The problem is at first simplified into a fixed point problem which can be solved by Brouwer's fixed point theorem. The solutions of the simplified problem are then continued via index-theory to solutions of approximate problems. In the final step it is proven that the solutions of the approximate problems have a limit point which corresponds to a solution of the original problem.