Standing wave solutions for a system derived from the Fitzhugh-Nagumo equations for nerve conduction
Standing wave solutions for a system derived from the Fitzhugh-Nagumo equations for nerve conduction
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从神经传导的 Fitzhugh-Nagumo 方程导出的系统的驻波解
DOI：
10.1137/0517009
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发表时间：
1986
影响因子：
2
通讯作者：
E. Mitidieri
中科院分区：
文献类型：
--
作者：
G. Klaasen;E. Mitidieri
我们将注意力集中在反应扩散系统$u_t = D_1 \Delta u + f(u) - v,$$v_t = D_2 \Delta v + \varepsilon (u - \gamma v)$上，其中$f(u) = u(1 - u)(u - a),0 < a < \frac{1}{2}$和$D_1 $, $D_2 $, $\varepsilon $, $\gamma $是正常数。参数$\gamma $选得很大，以便相关的动力学方程$(D_1 = D_2 = 0)$有三个常数解，其中两个是稳定的。给出了该系统的Dirichlet问题具有两个非平凡时无关解的充要条件。
We focus our attention on the reaction-diffusion system $u_t = D_1 \Delta u + f(u) - v,$$v_t = D_2 \Delta v + \varepsilon (u - \gamma v)$ where $f(u) = u(1 - u)(u - a),0 < a < \frac{1}{2}$ and $D_1 $, $D_2 $, $\varepsilon $, $\gamma $ are positive constants. The parameter $\gamma $ is chosen large so that the associated dynamic equations $(D_1 = D_2 = 0)$ have three constant solutions two of which are stable. The authors establish necessary and sufficient conditions that the Dirichlet problem for this system possesses two nontrivial time independent solutions.