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Science China Mathematics 2022年第2期65卷 291-308页

作者： Qian Yang mingkang ni School of Mathematical Sciences East China Normal UniversityShanghai 200241China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A piecewise-smooth second-order singularly perturbed differential equation whose right-hand side is a nonlinear function with a discontinuity on some curve is investigated. This is a new class of problems in the case where the degenerate equation has a multiple root on the left-hand side of the curve which separates the domain and an isolated root on the right-hand side of that curve. The asymptotics of a solution with an internal layer near a point on the discontinuous curve and the transition point is constructed. The method to construct the internal layer function is proposed. The behavior of the solution in the internal layer consisting of four zones essentially differs from the case of isolated roots. For sufficiently small parameter values, the existence of a smooth solution with an internal layer from the multiple root of the degenerate equation to the isolated root in the neighborhood of a point on the discontinuous curve is proved. The method can be shown to be effective in the given example.

关键词： reaction-diffusion equation multizonal internal layer asymptotic method piecewise-smooth dynamical system

STEP-LIKE CONTRAST STRUCTURE OF SINGULARLY PERTURBED OPTIMAL CONTROL PROBLEM＊

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Journal of Computational Mathematics 2012年第1期30卷 2-13页

作者： mingkang ni Limeng Wu Department of Mathematics East China Normal UniversityShanghai 200241China

The existence of step-like contrast structure for a class of singularly perturbed optimal control problem is presented by contrast structure theory. By means of direct scheme of boundary function method, we construct the uniformly valid asymptotic solution for the singularly perturbed optimal control problem. As an application, an example is given to illustrate the main result in this paper.

关键词： Singular perturbation Optimal control problem Contrast structure.

Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation

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Chinese Annals of Mathematics,Series B 2023年第1期44卷 81-98页

作者： Qian YANG mingkang ni College of Science University of Shanghai for Science and TechnologyShanghai 200093China School of Mathematical Sciences East China Normal UniversityShanghai 200062China Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice Shanghai 200241China

A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is *** existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is *** efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is *** sufficiently small parameter values,the existence theorem is proved by the technique of matching asymptotic *** example is given to show the effectiveness of their method.

关键词： Reaction-Diffusion-Advection equation Internal layer Asymptotic method Piecewise-Smooth dynamical system

On higher-dimensional contrast structure of singularly perturbed Dirichlet problem

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Science China Mathematics 2012年第3期55卷 495-507页

作者： ni mingkang WANG ZhiMing Department of Mathematics East China Normal University Shanghai 200241 China E-Institutes of Shanghai Universities at Shanghai Jiao Tong University Shanghai 200240 China

In this paper,we address the existence and asymptotic analysis of higher-dimensional contrast structure of singularly perturbed Dirichlet *** on the existence,an asymptotical analysis of a steplike contrast structure (i.e.,an internal transition layer solution) is studied by the boundary function method via a proposed smooth *** the framework of this paper,we propose a first integral condition,under which the existence of a heteroclinic orbit connecting two equilibrium points is ensured in a higher-dimensional fast phase ***,the step-like contrast structure is constructed,and the internal transition time is ***,the uniformly valid asymptotical expansion of such an available step-like contrast structure is ***,an example is presented to illustrate the result.

关键词： higher-dimensional contrast structure singular perturbation internal layer heteroclinic orbit

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一类具有转点的右端不连续奇摄动边值问题

应用数学和力学 2024年第4期45卷 470-489页

作者：帅欣倪明康华东师范大学数学科学学院上海200241

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明... 详细信息

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明了右问题具有空间对照结构的解,并通过在间断点的光滑缝接,得到了原问题的渐近解.最后,通过一个算例验证了结果的正确性.

关键词：奇摄动边值问题转点右端不连续空间对照渐近解

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