具有对流项的Hodgkin-Huxley方程粘性解的Cauchy问题  

The Cauchy Problem of Viscosity Solutions of Hodgkin-Huxley Equation with Convection Terms

作　　者：吴菲 WU Fei(College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 , China)

机构地区：[1]南京航空航天大学理学院,南京210016

出　　处：《西安文理学院学报（自然科学版）》2019年第3期1-5,14,共6页Journal of Xi’an University(Natural Science Edition)

摘　　要：讨论了具有对流项的Hodgkin-Huxley方程的粘性解的整体存在性.首先,利用自相似变换得到了原问题线性齐次化方程的解;然后,利用Duhamel原理和皮卡逐次逼近法给出了原Cauchy问题的局部解的存在唯一性;最后,利用极值原理获得了解的L~∞估计,从而证明了具有对流项的Hodgkin-Huxley方程的Cauchy问题粘性解的整体存在性.In this paper, the global existence of viscous solutions of Hodgkin-Huxley equation with convection term is discussed. Firstly, the solution of the linear homogenization equation of the original problem is obtained by using self-similar transformation. Then, the existence and uniqueness of local solutions of the original Cauchy problem are given by using Duhamel principle and Picca successive approximation method. Finally, the L^∞ estimate of solutions are obtained by using the extremum principle, and the global existence of viscous solutions for Cauchy problem of Hodgkin-Huxley equation with convection term is proved.

关 键 词：双曲守恒律 Hodgkin-Huxley方程 极值原理 整体存在性 L^∞估计 

分 类 号：O175.27[理学—数学]