二阶半线性奇摄动边值问题的渐近解

研究不满足法向双曲条件的二阶半线性非自治奇摄动Dirichlet边值问题.首先,利用边界层函数法,构造了问题在两个区间端点的代数边界层,获得了形式渐近解;接着,利用上下解方法,证明了解的存在性、渐近解的一致有效性以及渐近解与精确解之间的误差估计.研究表明:通过对奇异摄动参数进行适当的尺度变换,一定条件下可处理任意退化的二阶半线性非自治奇摄动边值问题.最后,通过一个典型例子验证了理论结果的正确性.     

具有无穷边界值的二次非线性奇摄动边值问题的双边界层

研究了具有无穷边界值的二次非线性奇摄动边值问题的双边界层,利用边界层校正函数,构造其渐近解,并利用微分不等式理论,给出了一致有效渐近估计.最后给出算例验证了相关结论的正确性.     

椭圆型方程的内层和边界层渐近解

本文讨论了一类半线性椭圆型方程边值问题.利用微分不等式理论,研究了边值问题内层和边界层解的存在性和渐近性态.     

一个奇摄动微分方程非线性混合边值问题

研究了一个三阶半线性微分方程的奇摄动非线性混合边值问题.利用边界层函数法构造了该问题的形式渐近解,并采用微分不等式理论证明了解的存在性,给出了渐近解的误差估计,最后得出了边界层函数指数型衰减的结论.     

一类四阶非线性奇摄动方程的边界层问题

本文研究了一类四阶非线性奇摄动方程的边界层问题,利用在左右边界层的两次匹配,得出了原问题解的一致有效的渐近表达式.这个结果是奇摄动理论在研究高阶微分方程中的一个应用.     

具有多参数的奇摄动非线性边值问题的摄动解

讨论含多个参数的高阶非线性方程的摄动解,在适当的条件下,先构造出外部解,再根据不同的边界层,利用伸展变量和幂级数展开式理论,构造问题的形式渐近解,最后利用微分不等式理论证明渐近解的一致有效性和渐近形态,把奇摄动非线性问题中的参数推广到多个参数.     

一类非线性奇摄动系统的可解性及渐近解

研究了一类非线性微分系统的奇摄动边值问题.利用边界层校正法构造了形式渐近解和用微分不等式理论,证明了解的渐近展开式的一致有效性,得到了相应的定理,从而得到了原问题的可解性条件.     

一类奇摄动燃烧ROBIN问题解的渐近性态

讨论了一类奇摄动燃烧问题.利用伸长变量,构造了问题解的边界层和内部层,并且得到了形式渐近解.再利用微分不等式证明了解的一致有效性.     

一类四阶非线性奇摄动方程的边值问题

利用匹配渐近展开法,讨论了一类四阶非线性方程的具有两个边界层的奇摄动边值问题．引进伸长变量,根据边界条件与匹配原则,在一定的可解性条件下,给出了外部解和左右边界层附近的内层解,得到了该问题的二阶渐近解,并举例说明了这类非线性问题渐近解的存在性．     

一类非线性奇摄动方程解的渐近表示

应用匹配渐近方法讨论一类非线性奇异摄动方程的边值问题解的渐近表示,得到了边界层或冲击层解的刻画,阐述了边界参数对边界层或冲击层位置的影响.     

具有多重解的非线性奇摄动问题

利用边界层法,研究了一类具有多重解的非线性奇摄动问题．在适当的假设下,通过给出外部解展开式系数及其对应边界条件的一般表达式,根据退化问题的边值作为某方程的根的重数,得到了此问题不同形式的渐近解．特别地,当这种根的重数为偶数时,问题具有二重解．另外,将相关结果应用于化学反应器理论,并通过对具有多重解的例子的渐近解和精确解的数值模拟说明如此构造的渐近解具有较高的精度．     

Large solutions for quasilinear elliptic equation with nonlinear gradient term

We study the existence, asymptotic behavior near the boundary and uniqueness of large solutions for a class of quasilinear elliptic equation with a nonlinear gradient term. By constructing the suitable blow-up upper and lower solutions, we obtain the existence and the asymptotic behavior of radial large solutions of the problem in balls and then derive the existence of solutions in a general domain by a comparison argument. By using a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of any nonnegative solution of it near the boundary. The uniqueness is shown by a standard argument.     

催化反应中的一类奇摄动边值问题

§1. Introduction We are concered with the singularly perturbed boundary value problemε2y″=y3,(1)y(0)=1, y(1)=2,(2)where ε＞0 is a positive small parameter. This problem arises as models for certain catalytic reactions in chemical engineering. The study of that problem has been paid much attention for the boundary layers of the problem exihibit the behavior of nonexponential decay. There have been some works on this subject ［1］-［4］. In particular, Howes and Chang［1］ gave an accurate…     

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.     

Artificial boundary conditions for Petrovsky systems of second order in exterior domains and in other domains of conical type

The approximation of solutions to boundary value problems on unbounded domains by those on bounded domains is one of the main applications for artificial boundary conditions. Based on asymptotic analysis, here a new method is presented to construct local artificial boundary conditions for a very general class of elliptic problems where the main asymptotic term is not known explicitly. Existence and uniqueness of approximating solutions are proved together with asymptotically precise error estimates. One class of important examples includes boundary value problems for anisotropic elasticity and piezoelectricity. Copyright © 2004 John Wiley & Sons, Ltd.     

ASYMPTOTIC SOLUTIONS OF THE ELASTIC EQUATION IN THE CASE OF TOTAL REFLECTION

In this paper we construct outgoing asymptotic solutions of the anisotropic elastic wave equation coinciding with given data on the boundary when total reflection happens. In this case the solutions consist of the usual hyperbolic parts and the elliptic parts exponentially decreasing in the normal direction to the boundary. The main assertion is that sum of those parts can cover any boundary data because of the elasticity. The proof is reduced to the complex analysis of the symbol of the elastic operator. By means of the asymptotic solutions we can make parametrices and study propagation of the singularities in the case of total reflection.

     

具有边界摄动的非线性非局部反应扩散方程的奇摄动问题

A class of nonlinear nonlocal singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained; secondly, by using the stretched variable, the composing expansion method and the expanding theory of power series, the initial layer is constructed; and finally, by using the theory of differential inequalities the asymptotic behavior of solutions for initial boundary value problems is studied, and including some relational inequalities the existence and uniqueness of solutions for the original problem and the uniformly valid asymptotic estimation are discussed.     

A method of asymptotic expansions of the solutions of the steady heat conduction problem for laminated non-uniform anisotropic plates

Outer asymptotic expansions of the solutions of the steady heat conduction problem for laminated anisotropic non-uniform plates for different boundary conditions on the faces are constructed. The two-dimensional resolvents obtained are analysed and the asymptotic properties of the solutions of the heat-conduction problem are investigated. Estimates are obtained of the accuracy with which the temperature in the plate outside the limits of the boundary layer can be assumed to be piecewise-linearly or piecewise-quadratically distributed over the thickness of the laminated structure. A physical justification for certain features of the asymptotic expansions of the temperature is given.     

Asymptotic periodicity of a food-limited diffusive population model with time-delay

In this paper, a general reaction-diffusion food-limited population model with time-delay is proposed. Accordingly, the existence and uniqueness of the periodic solutions for the boundary value problem and the asymptotic periodicity of the initial-boundary value problem are considered. Finally, the effect of the time-delay on the asymptotic behavior of the solutions is given.     

Asymptotics of the eigenvalues of a boundary value problem for a vector singular differential equation

By analyzing a system of integro-differential equations of the Volterra-Stieltjes type, for large parameter values, we obtain asymptotic formulas for a linearly independent system of solutions of ordinary differential equations with generalized functions in coefficients. These solutions permit one to construct asymptotic formulas for the eigenvalues of a boundary value problem in the case of regular boundary conditions.