From the Boundary of the Convex Core to the Conformal Boundary

If N is a hyperbolic 3-manifold with finitely generated fundamental group, then the nearest point retraction is a proper homotopy equivalence from the conformal boundary of N to the boundary of the convex core of N. We show that the nearest point retraction is Lipschitz and has a Lipschitz homotopy inverse and that one may bound the Lipschitz constants in terms of the length of the shortest compressible curve on the conformal boundary.     

非特征边界的MHD方程的边界层

考查了小粘性时非特征边界情况下MHD方程在边界附近的性质,说明速度在边界上不为零.源于之前非特征边界条件下不可压缩Navier-Stokes方程边界层的工作,证明了边界层的存在性,并得到了当粘性收敛于零时,MHD方程的解收敛于理想MHD方程的解.     

Boundary Estimates for Solutions of the Parabolic Free Boundary Problem

Let u and solve the problem

Navier边界条件下湖方程的边界层问题

考虑光滑区域上二维粘性湖方程在Navier边界条件下的无粘极限问题,证明了具有Navier边界条件粘性湖方程的边界层在Sobolev空间中是非线性稳定的,验证了具有较弱强度的边界层的渐近展开的合理性.     

Boundary Layer Solution of the Boltzmann Equation for Specular Boundary Condition

In the paper, we establish the existence of steady boundary layer solution of Boltzmann equation with specular boundary condition in L_x,v²∩L_x,v^∞in half-space. The uniqueness, continuity and exponential decay of the solution are obtained, and such estimates are important to prove the Hilbert expansion of Boltzmann equation for half-space problem with specular boundary condition.     

边界条件含参数的二阶奇异非线性边值问题

利用不动点指数理论以及上下解方法得到了边界条件含参数的二阶奇异非线性边值问题的正解存在性结果，该结果推广了已有文献中的众多结果．     

Boundary Value Problems with Compatible Boundary Conditions

If Y is a subset of the space ℝⁿ × ℝⁿ, we call a pair of continuous functions U, V Y-compatible, if they map the space ℝⁿ into itself and satisfy Ux · Vy ≥ 0, for all (x, y) ∈ Y with x · y ≥ 0. (Dot denotes inner product.) In this paper a nonlinear two point boundary value problem for a second order ordinary differential n-dimensional system is investigated, provided the boundary conditions are given via a pair of compatible mappings. By using a truncation of the initial equation and restrictions of its domain, Brouwer's fixed point theorem is applied to the composition of the consequent mapping with some projections and a one-parameter family of fixed points P _δ is obtained. Then passing to the limits as δ tends to zero the so-obtained accumulation points are solutions of the problem.     

Boundary Value Problems with Local Generalized Nevanlinna Functions in the Boundary Condition

For a class of abstract λ-dependent boundary value problems where a local variant of generalized Nevanlinna functions appears in the boundary condition, linearizations are constructed and their local spectral properties are investigated.     

When Does the Free Boundary Enter into Corner Points of the Fixed Boundary?

Our prime goal in this note is to lay the ground for studying free boundaries close to the corner points of a fixed Lipschitz continuous boundary. Our study is restricted to 2-space dimensions and to the obstacle problem. Our main result states that the free boundary cannot enter a corner x⁰ of the fixed boundary if the (interior) angle is less than π, provided that the boundary datum is zero near to the point x⁰. For larger angles and other boundary data, the free boundary may enter into corners, as discussed in the text. Bibliography: 10 titles. To Nina Nikolaevna Uraltseva on the occasion of her 70th birthday __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 213–225.     

关于边界层方法

本文指出传统的边界层方法(包括匹配法和Vi?ik—Lyusternik方法)的不足:不能作出边界层项的渐近展开式.提出多重尺度构造边界层项的方法,得到符合实情的结果.又与Levinson所用的方法比较,本方法能更简单地导出后一方法给出的边界层项的渐近展开式.又应用此方法研究现有的关于奇异摄动的某些成果,指出这些成果的局限性,并在一般情况下作出解的渐近展开式.     

Boundary interpolation in the ball

We solve a boundary interpolation problem in the reproducing kernel Hilbert space of functions analytic in the unit ball of with reproducing kernel 1/(1−∑₁^Nz_kw_k^*). We introduce the notion of Brune factor (or Blaschke–Potapov factor of the third kind) in this setting.     

Power Boundary Layers in the Averaging Problem for a Scalar Equation Degenerate on the Boundary

A full asymptotic expansion of a solution to a second-order equation with rapidly oscillating coefficients in a rectangle is constructed. The Dirichlet boundary conditions are imposed on those sides of the rectangle on which the coefficients may degenerate, whereas the periodicity conditions are imposed on the remaining sides. The boundary layers may decrease only polynomially far from _±. Bibliography: 52 titles.     

Exact Boundary Controllability for the Spatial Vibration of String with Dynamical Boundary Conditions

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact boundary controllability of this system by means of a constructive method with modular structure.     

A New Boundary Element Method for the Biharmonic Equation with Dirichlet Boundary Conditions

We consider a scalar boundary integral formulation for the biharmonic equation based on the Almansi representation. This formulation was derived by the first author in an earlier paper. Our aim here is to prove the ellipticity of the integral operator and hence establish convergence of and error bounds for Galerkin boundary element methods. The theory applies both in two and three dimensions, but only for star-shaped domains. Numerical results in two dimensions confirm our analysis.     

On a Singular Semilinear Elliptic Boundary Value Problem and the Boundary Harnack Principle

On a bounded C ²-domain we consider the singular boundary-value problem 1/2u=f(u) in D, u _D =, where d3, f:(0,)(0,) is a locally Hölder continuous function such that f(u) as u0 at the rate u ^–, for some (0,1), and is a non-negative continuous function satisfying certain growth assumptions. We show existence of solutions bounded below by a positive harmonic function, which are smooth in D and continuous in . Such solutions are shown to satisfy a boundary Harnack principle.     

连铸中的自由边界问题的边界元解法

本文应用边界元法求解钢铁生产中连铸工艺出现的自由边界问题。首先,对较一般的连铸过程的数学模型进行简化并给出相应的边界积分方程,以及叙述了用边界元法求解该问题的步骤。然后,我们给出了一个计算实例,并对该方法的收敛快慢、对初值的敏感性和对区域形状的适应性等问题进行了探讨。最后,针对一种简化的模型,将数值解与解析解进行比较,两者吻合较好。     

Boundary Control of PDEs via Curvature Flows: the View from the Boundary, II

We describe some results on the exact boundary controllability of the wave equation on an orientable two-dimensional Riemannian manifold with nonempty boundary. If the boundary has positive geodesic curvature, we show that the problem is controllable in finite time if (and only if) there are no closed geodesics in the interior of the manifold. This is done by solving a parabolic problem to construct a convex function. We exhibit an example for which control from a subset of the boundary is possible, but cannot be proved by means of convex functions. We also describe a numerical implementation of this method.     

源于膨胀波边界层理论中的一类奇异边值问题

对源于膨胀波边界层理论中的一类奇异边值问题进行了研究,利用单调逼近方法得到了满足物理意义上正解的存在性和唯一性的充分条件,同时给出了用速度比例参数表示的壁摩擦的估计公式, 利用打靶法技巧得到了问题的数值解.数值结果证明了估计公式的可靠性和有效性.     

The Set of Pre-Ends and the Ideal Boundary of a Manifold without Boundary

Relations between prime pre-ends and elements of the ideal boundary of a manifold without boundary are studied. The cases of a manifold with Mazurkiewicz or Riemannian intrinsic metric and of a manifold with quasihyperbolic metric are considered.