Minimizing sequences of variational problems with small parameters

A class of variational problems with small parameters is studied. Their zeroth-order asymptotic solutions are constructed. It is shown that the zeroth-order asymptotic solution is just the minimizing sequence of variational problems as the small parameter approaches to zero.     

具有快慢层的非光滑奇异摄动问题的空间对照结构

该文研究了具有快慢层的非光滑奇异摄动问题的空间对照结构.利用边界层函数法构造了该问题的形式渐近解,并运用"缝接法"证明了问题光滑解的存在性以及渐近解的一致有效性.最后,通过例子验证了所得结果的有效性.     

PERIODIC SOLUTION TO A KIND OF SINGULARLY PERTURBED DIFFERENTIAL EQUATIONS OF PARABOLIC TYPE IN CHEMICAL KINETICS

This paper deals with the problem on the periodic solution for the singularly perturbeddifferential equations of parabolic type originating from chemical kinetics in stratifiedmedia,A uniformly valid asymptotic solution is constructed and the related asymptoticestimate is given.     

Step-like contrast structure for class of nonlinear singularly perturbed optimal control problem

The step-like contrast structure for a class of nonlinear singularly perturbed optimal control problems is considered. The existence of the step-like contrast structure for the singularly perturbed optimal control problem is proved by equivalence, which is based on the necessary conditions. The authors not only give the conditions under which there exists a step-like contrast structure, but also determine where the internal transition time is. Meanwhile, the uniformly valid asymptotic expansion of the step-like contrast structure solution is constructed by the direct scheme method. Finally, an example is presented to show the result.     

经典物理中的扰动时滞模型解

利用边界层函数法研究了一类经典物理中的扰动时滞模型. 构造了模型解的渐近表达式, 并讨论了它的渐近性态. 关键词： 经典物理 扰动 近似解     

具有不连续源的奇摄动边值问题

本文研究了具有不连续源的奇摄动边值问题.利用边界层函数法和缝接法,得到了整个区间上原问题解的一致有效的渐近表达式.     

Contrast structure for singular singularly perturbed boundary value problem

The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step- type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.     

具有代数衰减的边界层问题

本文研究了不满足Tikhnov定理中稳定性要求的一类常微分方程奇摄动边值问题.利用边界层函数法以及微分不等式理论,分别构造了渐进解的形式和证明了解的存在性和渐近解一致有效性并进行了余项估计,得出了该类问题边界层代数式衰减的结论.     

一类线性奇异摄动最优控制问题的渐近解

研究了一类线性奇异摄动最优控制问题的空间对照结构,讨论了初始点固定,终端自由的情形.首先根据变分法得到了一阶最优性条件,其次运用退化最优控制问题的解证明了异宿轨道的存在性,从而结合奇异摄动理论证明了原问题空间对照结构解的存在性.进一步根据解的结构,利用边界层函数法构造了奇异摄动最优控制问题一致有效的形式渐近解.最后,通过例子验证了结果的可行性.     

带有小参数变分问题的极小化序列

针对一类含有小参数的变分问题构造了零次渐近解,并证明了当小参数趋向于0时,该零次渐近解就是原问题的极小化序列.