非线性奇摄动边值问题的零次渐近展开式研究  

Zero Asymptotic Expansion of Nonlinear Singularly Perturbed Boundary Value Problems

作　　者：张媛 

机构地区：[1]重庆邮电大学移通学院,重庆401520

出　　处：《湘潭大学自然科学学报》2018年第1期48-52,共5页Natural Science Journal of Xiangtan University

基　　金：重庆市高等教育教学改革研究项目(153201)

摘　　要：对非线性奇摄动边值问题的零次渐近展开式进行了研究.首先,构建了一类具有齐次双曲波动扰动项的非线性奇摄动方程,并对方程进行边值稳定性求解.然后,采用Lyapunove稳定性泛函理论对方程的双孤波解向量进行线性回归处理,结合最小二乘拟合方法进行边值向量的零次渐近展开.在全局有限时间域内得到零次渐近展开式的Lipschitz连续正则项,结合超临界稳定性原理进行非线性奇摄动边值零次渐近展开的稳定性和收敛性证明.推导得知,非线性奇摄动方程的边值项通过零次渐近展开,在时滞控制过程中是渐进收敛和超临界稳定的.The nonlinear singularly perturbed boundary value problem of zero asymptotic expansion is studied.A nonlinear singularly perturbed equation with homogeneous hyperbolic perturbation term is constructed,and the boundary value stability of the equation is solved.Lyapunove stability functional theory is used to deal with double solitary wave solution vector of equation,and the zero order asymptotic expansion of the boundary value vector is fitted by least square method.The Lipschitz continuous regular term of zero asymptotic expansion is obtained in the global finite time domain.The stability and convergence of nonlinear singularly perturbed boundary zero asymptotic expansion are proved combination with the principle of supercritical stability.The boundary value terms of nonlinear singularly perturbed equations are asymptotically convergent and asymptotically stable in time delay control process by zero order asymptotic expansion.

关 键 词：非线性 边值问题 临界稳定 时滞控制 摄动 

分 类 号：O175.27[理学—数学]