一类非线性拟双曲方程的初边值问题  

Initial boundary value problem for a class of nonlinear quasi-hyperbolic equation

作　　者：刘亚成[1] 郭秀芳[1] 

机构地区：[1]哈尔滨工程大学理学院,哈尔滨150001

出　　处：《黑龙江大学自然科学学报》2008年第1期46-49,共4页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10271034);哈尔滨工程大学基础研究基金资助项目(HEUF04012)

摘　　要：用Galerkin方法结合能量估计研究任意维数的神经传播型非线性拟双曲方程的初边值问题。证明了当n≤3时,对非线性项在某些条件下,问题能得到整体时间L∞强解,当n≥4时,在f∈C,g∈C1,f,g′下方有界,f,g满足一定的增长条件下,问题得到了整体时间L2强解。根据需要,在n≥4时,引进了一种新的整体强解的概念,从实质上推广了文献[1]的结果。The initial boundary value problem for nonlinear quasi - hyperbolic equation of nerve conduction type in arbitrary dimensions is studied by Galerkin method together with energy estimate. It is proved that when n≤3, the problem has a global time L^∞ strong solution if nonlinear terms be in some conditions. When n ≥4, the problem has a global time L^2 strong solution if f∈C,g∈C^1, fand g＇are bounded from below, fand g satisfy certain growth condition. According to the demand, a new concept of Global strong solution is introduced when n ≥4. It generalizes the result of the first reference in essence.

关 键 词：神经传播型 非线性 拟双曲方程 初边值问题 强解 

分 类 号：O175.26[理学—数学]