| 具有周期边界的Fitzhugh-Nagumo方程的初边值问题 |
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| 引用本文： | 申伟杰,柴玉珍. 具有周期边界的Fitzhugh-Nagumo方程的初边值问题[J]. 中北大学学报(自然科学版), 2012, 0(3): 228-231 |
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| 作者姓名： | 申伟杰 柴玉珍 |
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| 作者单位： | 太原理工大学数学学院 |
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| 基金项目： | 太原理工大学校科技发展基金资助项目(博士启动费) |
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| 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方程的一种简化.讨论了Fitzhugh-Nagumo方程具有周期边界的初边值问题,利用Galerkin方法及常微分方程理论,证明了具有周期边界的Fitzhugh-Nagumo方程存在局部解,通过对局部解作一致先验估计证明了整体解的存在性;利用Gronwall不等式证明了Fitzhugh-Nagumo方程整体解的唯一性.
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| 关 键 词： | Fitzhugh-Nagumo方程 Galerkin方法 Gronwall不等式 |
Initial Value Problem for Fitzhugh-Nagumo Equations with Periodic Boundary |
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| SHEN Wei-jie,CHAI Yu-zhen. Initial Value Problem for Fitzhugh-Nagumo Equations with Periodic Boundary[J]. Journal of North University of China, 2012, 0(3): 228-231 |
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| Authors: | SHEN Wei-jie CHAI Yu-zhen |
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| Affiliation: | (College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China) |
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| Abstract: | Hodgkin-Huxley equations are the differential equations that describing the relationship between membrane currents and voltages in nerve fibers.Fitzhugh-Nagumo equations are the simplification of Hodgkin-Huxley equations.The initial value problem of Fitzhugh-Nagumo equations with periodic boundary was discussed.The existence of local solutions to the Fitzhugh-Nagumo equations with periodic boundary was proved by means of the Galerkin method and the theory of ordinary differential equation.And the existence of global solutions was also proved through prior estimates of local solutions.Its uniqueness of the global solutions was proved by using Gronwall inequality. |
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| Keywords: | Fitzhugh-Nagumo equations Galerkin menthod Gronwall inequality |
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