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 Layers and Boundary Hinge-Support Conditions for Thin Plates

The boundary-layer phenomenon is investigated for a thin three-dimensional plate. An arbitrary anisotropy of elastic properties and nonhomogeneity in longitudinal and transversal directions are assumed. Several initial asymptotic terms are constructed and a way of continuing the asymptotic procedure is described. Precise estimates of the difference between the exact and approximate solutions are obtained for the energy norm. An amalgamated problem is formed that gives the two-term asymptotics of the fields of displacements and stresses at a distance from the lateral side of the plate, whereas the edge effects are simulated by conditions of elastic fastening containing integral characteristics of the boundary-layer problem in the semistrip. Hinge-support conditions due to a sufficiently narrow clamped zone at the edge of the plate are derived and justified as well. Bibliography: 48 titles.     

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.     

奇异边值问题的边界非正则正解

本文讨论一类二阶奇异边值问题正解的存在性．证明了这类问题存在边界非正则正解．     

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.     

Three-Dimensional Boundary Value Problems of Elastothermodiffusion with Mixed Boundary Conditions

We investigate the basic boundary value problems of the connected theory of elastothermodiffusion for three-dimensional domains bounded by several closed surfaces when the same boundary conditions are fulfilled on every separate boundary surface, but these conditions differ on different groups of surfaces. Using the results of papers [1–8], we prove theorems on the existence and uniqueness of the classical solutions of these problems.     

Boundary Estimates for Solutions of the Parabolic Free Boundary Problem

Let u and solve the problem

Noninvariant Boundary Conditions

It is generally believed that in order to solve initial and boundary value problems using Lie symmetry methods, the boundary and initial conditions need to be left invariant by the infinitesimal symmetry generator which admits the invariant solution. In this article we give less restrictive conditions on the imposed initial and boundary values in order that they be recoverable with a particular symmetry generator.     

Boundary in context

A contextualist account of modal assertions is sketched that makes their truth sensitive to the presuppositions of the conversation. Support for the account is mustered by considering its application to the context-sensitivity of assertions of subjunctive conditional sentences, explanation sentences, and knowledge sentences.     

SLE Boundary Visits

We study the probabilities with which chordal Schramm–Loewner evolutions (SLE) visit small neighborhoods of boundary points. We find formulas for general chordal SLE boundary visiting probability amplitudes, also known as SLE boundary zig-zags or order refined SLE multi-point Green’s functions on the boundary. Remarkably, an exact answer can be found to this important SLE question for an arbitrarily large number of marked points. The main technique employed is a spin chain–Coulomb gas correspondence between tensor product representations of a quantum group and functions given by Dotsenko–Fateev type integrals. We show how to express these integral formulas in terms of regularized real integrals, and we discuss their numerical evaluation. The results are universal in the sense that apart from an overall multiplicative constant the same formula gives the amplitude for many different formulations of the SLE boundary visit problem. The formula also applies to renormalized boundary visit probabilities for interfaces in critical lattice models of statistical mechanics: we compare the results with numerical simulations of percolation, loop-erased random walk, and Fortuin–Kasteleyn random cluster models at Q = 2 and Q = 3, and find good agreement.     

边界条件带导数的积分边值问题的正解

研究如下二阶积分边值问题的正解:■其中f∈C([0,1]×R~+,R~+).在先验估计的基础上,利用不动点指数理论建立了正解的存在性和多重正解的存在性.     

二阶非线性常微分方程积分边值条件四点边值问题正解

本文证明二阶非线性常微分方程积分边值条件四点边值问题正解的存在性。     

Laplace方程边值问题的边界积分方程法

§ 1.　Introduction　　Inengineeringandtechnology ,theproblemofstaticelectricfieldscanbeattributedtotheboundaryproblemofLaplaceequationofstaticeletricpotentialfunction .Themethodsofclassi calmathematicalphysicscanbeonlyusedtosolveboundaryproblemofverysimpledomainandspecialboundarycondition .Althoughthemethodsoflimitedelementscanbeusedtosolvetheproblemsonarbitrarydomain ,butitneedstopartitionthewholedomainandtocalculateverycomplex .Theapproachofboundaryintegralequationistosolverelatedproblemsb…     

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.     

具有非线性边界条件的向量边值问题的奇摄动

该文利用微分不等式理论证明了具有非线性边界条件的非线性系统摄动解的存在，并给出了解的按分量直到O（εN 1）的一致有效的估计．     

Discontinuous Boundary Value Problems with Retarded Argument and Eigenparameter-Dependent Boundary Conditions

In this paper we study the asymptotic formulas for the eigenvalues and corresponding eigenfunctions of discontinuous boundary value problems with retarded argument and eigenparameter-dependent boundary conditions.     

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.