Some Boundary — Contact Problems of the Elasticity Theory with Mixed Boundary Conditions Outside the Contact Surface

n — Dimensional (n ≥ 2) boundary-contact problems of statics of the elasticity theory for homogeneous anisotropic media are investigated when the contact of two bounded domains occurs from the outside on some part of boundaries with mixed boundary conditions. Theorems on the existence and uniqueness of solutions of boundary-contact problems in Besov and Bessel potential spaces are obtained. The smoothness of solutions is studied in closed domains occupied by elastic media.     

Banach空间中二阶微分方程Neumann边值问题的解

本文在序Banach空间中讨论二阶非线性微分方程的Neumann边值问题 :-u″=f(t,u) ,u′( 0 ) =u′( 1 ) =θ.在上下解反向给定时 ,利用半序理论和新的比较原理 ,证明了此Neumann边值问题最小解和最大解的存在性 ,解的唯一性 ,并给出了唯一解的近似迭代序列的误差估计式 .     

Boundary Equations in Dynamic Problems of the Theory of Elasticity

We study various nonstationary boundary equations that arise when the mixed problems of the theory of elasticity and thermoelasticity are solved by means of dynamic surface potentials. In the review, the results obtained are presented on their unique solvability in the scales of function spaces of the Sobolev type.     

A Calculus of Boundary Value Problems in Domains with Non–Lipschitz Singula Points

The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.     

The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary

In this paper we propose a method for solving the mixed boundary-value problem for the Laplace equation in a connected exterior domain with an arbitrary partition of the boundary. All simple closed curves making up the boundary are divided into three sets. On the elements of the first set the Dirichlet condition is given, on the elements of the second set the third boundary condition is prescribed, and the third set, in turn, is divided into two subsets of simple closed arcs, with the Dirichlet condition prescribed on the elements of one of these subsets and the third boundary condition on the elements of the other subset. The problem is reduced to a uniquely solvable Fredholm equation of the second kind in a Banach space. The third boundary-value problem and the mixed Dirichlet--Neumann problem are particular cases of the problem under study.     

On the Calderón problem in periodic cylindrical domain with partial Dirichlet and Neumann data

We consider the Calderón problem in an infinite cylindrical domain, whose cross section is a bounded domain of the plane. We prove log–log stability in the determination of the isotropic periodic conductivity coefficient from partial Dirichlet data and partial Neumann boundary observations of the solution. Copyright © 2017 John Wiley & Sons, Ltd.     

Plane Waves and Boundary Value Problems in the Theory of Elasticity for Solids with Double Porosity

This paper concerns with the dynamical theory of elasticity for solids with double porosity. This theory unifies the earlier proposed quasi-static model of Aifantis of consolidation with double porosity. The basic properties of plane waves are established. The radiation conditions of regular vectors are given. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated. The uniqueness theorems are proved. The basic properties of elastopotentials are given. The existence of regular (classical) solution of the external BVP by means of the potential method (boundary integral method) and the theory of singular integral equations are proved.     

Banach空间中高阶常微分方程初边值问题的可解性

利用基于度理论的不动点定理,该文给出了Ｂａｎａｃｈ空间中ｎ阶常微分方程的初、边值问题有解的某些充分条件,同时证明了一类最大最小解的存在性．推广了现有文献中的某些结果．     

含间断项的微分方程终值问题的拟上下解方法

在不涉及紧型条件的情形下,利用半序理论和混合单调迭代技术研究了Banach空间中含间断项的一阶微分方程终值问题解的存在唯一性;并给出逼近解迭代序列的误差估计.     

上下解反序条件下二阶泛函微分方程Neumann边值问题解的存在性条件

主要利用上下解和单调迭代法,研究了带有N eum ann边界条件的二阶泛函微分方程在上下解反序条件下解的存在性条件.     

Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables

Engineering optimization problems are multicriteria with continuous, discrete, and mixed design variables. Correct definition of the feasible solution set is of fundamental importance in these problems. It is quite difficult for the expert to define this set. For this reason, the results of searching for optimal solutions frequently have no practical meaning. Furthermore, correct definition of this set makes it possible to significantly reduce the time of searching for optimal solutions. This paper describes construction of the feasible solution set with continuous, discrete, and mixed design variables on the basis of Parameter Space Investigation (PSI) method.