非自治Fitzhugh-Nagumo方程在周期边界下的整体解  

Integral Solution of Non-Autonomous Fitzhugh-Nagumo Equation Under the Periodic Boundary

作　　者：张珊 柴玉珍 

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2017年第5期531-535,共5页Journal of North University of China(Natural Science Edition)

摘　　要：Hodgkin-Huxley方程是描述神经纤维膜电流、膜电压关系的微分方程,Fitzhugh-Nagumo方程是Hodgkin-Huxley方程的简化模型.讨论了具有周期边界的非自治FitzHugh-Nagumo系统在外刺激下的初边值问题,首先利用Galerkin方法及常微分方程理论证明了具有周期边界的非自治Fitzhugh-Nagumo方程存在局部解;其次利用了一种新的方法对局部解作一致先验估计证明了整体解的存在性;最后利用Gronwall不等式证明了非自治Fitzhugh-Nagumo系统整体解的唯一性.Hodgkin-Huxley is a kind of differential equation describes the relations of nerve fiber membrane electric current and the membrane voltage and it is a simplified model of Hodgkin-Huxley.The initial-boundary value problem of non-autonomous Fitzhugh-Nagumo system with periodic boundary under the external stimulation is discussed.Firstly,using the Galerkin method and theory of ordinary differential equations the existence of local solution of non-autonomous Fitzhugh-Nagumo equations with periodic boundary;Secondly,with a new method of local solution for consistent prior estimate proves the existence of global solution;Finally,using Gronwall inequality proves the uniqueness of global solutions of non-autonomous Fitzhugh-Nagumo system as a whole.

关 键 词：Fitzhugh-Nagumo系统 非自治方程 外刺激项 GALERKIN方法 GRONWALL不等式 

分 类 号：O241.8[理学—计算数学]