一类Stefan问题的渐近解

本文讨论了一类具有一般初值条件的Stefan问题.把研讨论板分成三部份,每一部份选用不同的时间尺度,然后用PLK方法或类多重尺度法求得每一部份的渐近解.最后,就此解进行了讨论并得出相应的结论.     

Asymptotic Solution of the Autoresonance Problem

We study the problem of forced oscillations near a stable equilibrium of a two-dimensional nonlinear Hamiltonian system of equations. A given exciting force is represented as rapid oscillations with a small amplitude and a slowly varying frequency. We study the conditions under which such a perturbation makes the phase trajectory of the system recede from the original equilibrium point to a distance of the order of unity. To study the problem, we construct asymptotic solutions using a small amplitude parameter. We present the solution for not-too-small values of time outside the original boundary layer.     

The Asymptotic Behaviour of the Solutions of a Degenerate Reaction-diffusion Problem

Consider in this paper the existence, uniqueness and asymptotic behaviour of the solutions of the mixed problem for a class of degenerate quasilincar parabolic equations and properties of the corresponding stationary solutions.     

弹性直杆中一类动力屈曲问题的渐近解

对于弹性杆受刚性块轴向撞击的动力屈曲问题而言,由于轴向载荷形式较为复杂,问题将归结为关于非线性偏微分方程组解的讨论,至今仍未能得到一个理论上的解析解,为此,讨论了有限长理想弹性直杆的此类动力屈曲问题,采用小参数的摄动展开和变分法,成功地得到了这一问题的一个理论上的近似解,并给出了相应的算例,从中得到了一些有益的结论.     

一个渐近非线性二阶两点边值问题的存在性

利用拓扑度理论获得了一个渐近非线性二阶两点边值问题的存在定理。     

一类正则Sturm—Liouville问题特征的渐近分析

考虑[0,π]上一类带一般分离型边界条件的正则Sturm—Liouville问题特征的渐近表示,利用Frechet导数,对特征值进行精细的分析,清楚地给出了方程系数q（x）及边界条件中常数cot α,col β对特征值的影响．使结论更具一般化．     

一类周期自由边界问题解的渐近性态

本文证明了化学反应扩散过程中的一类周期自由边界问题古典解的存在唯一性，并且讨论了潜热L→0时周期Stefan问题古典解的渐近性态及误差估计．     

Asymptotic Analysis of a Nonlinear Problem in Thermoelasticity

In this paper we employ our previously formulated constitutive relations for an elastic heat conductor to examine the nonlinear influence of the temperature on the propagation of second sound. Utilizing the method of geometric optics we ascertain that large values of second sound travel more slowly than do smaller ones. As well, numerical results for a signaling problem are displayed graphically in order to highlight the qualitative properties of the temperature and strain waves. The choice of signaling data was motivated by experimental studies.     

Existence of an Asymptotic Second－order Three－point Boundary Value Problem

By making use of degree theory， a new existence theorem is established for an asymptotic second-order three-point boundary value problem.     

Asymptotic Dirichlet Problem for Harmonic Maps with Bounded Image

Existence and uniqueness is proved for asymptotic Dirichlet problems on Hadamard manifolds. This includes manifolds of bounded negative curvature and symmetric spaces of higher rank.     

The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior

The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, u_t = u^m with m > 1, posed in a bounded domain of the n-dimensional space with homogeneous boundary conditions. Asymptotic profiles are obtained and full proofs of the convergence results are given. Solutions with changing sign and problems posed in tubes are also considered.     

The Dirichlet Problem for the Porous Medium Equation in Bounded Domains. Asymptotic Behavior

The paper contains a complete study of the large-time behavior of solutions of the Porous Medium Equation, u_t = u^m with m > 1, posed in a bounded domain of the n-dimensional space with homogeneous boundary conditions. Asymptotic profiles are obtained and full proofs of the convergence results are given. Solutions with changing sign and problems posed in tubes are also considered.     

一类非线性奇摄动Robin问题解的渐近性态

利用渐近理论和微分不等式的方法,该文研究了一类非线性奇摄动Robin问题. 证明了其解的存在性,并得到了解的任意n 阶一致有效渐近展开式.     

The Asymptotic Solution of a Connection Problem of a Second Order Ordinary Differential Equation

The solutions of the equation are discussed in the limit ρ → 0. The solutions which oscillate about ? |t| as t → ∞ have asymptotic expansions whose leading terms are where Ã₊, , Ã_?, and are constants. The connection problem is to determine the asymptotic expansion at + ∞. In other words, we wish to find (Ã₊, ) as functions of Ã_? and The nonlinear solutions with Ã_± not small are analyzed by using the method of averaging. It is shown that this method breaks down for small amplitudes. In this case a solution can be obtained on [0, ∞) as a small amplitude perturbation about the exact nonoscillating solution W(t) whose asymptotic expansion is This is a solution of (1) which corresponds to Ã₊ ≡ 0 in (2). A quantity which determines the scale of the small amplitude response is ?W'(0). This quantity is found to be exponentially small. The determination of this constant is shown to reduce to a solution of the equation for the first Painlevé transcendent. The asymptotic behavior of the required solution is determined by solving an integral equation.     

About Asymptotic Behavior for a Transmission Problem in Hyperbolic Thermoelasticity

We consider a transmission problem in thermoelasticity with memory. We show the exponential decay of the solution in case of radially symmetric situations, as time goes to infinity.      

Asymptotic Boundary Value Problem of Harmonic Maps via Harmonic Boundary

We prove that given any continuous data f on the harmonic boundary of a complete Riemannian manifold with image within a ball in the normal range, there exists a harmonic map from the manifold into the ball taking the same boundary value at each harmonic boundary point as that of f.     

常差分方程奇异摄动问题的渐近方法

在本文中,我们讨论如下差分方程问题(P_ε):(L.y)_k≡εy(k+1)+a(k,ε)y(k)+b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1)B₁y≡-y(0)+c₁y(1)=a,B₂y≡-c₂y(N-1)+y(N)=β这里ε是一个小参数,c₁,c₂,a,β为常数,a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)是k和ε的函数.首先,我们讨论了常系数的情形;接着引进伸长变换对变系数的情形进行了讨论,给出了解的一致渐近展开式;最后给出了一个数值例子.