The Initial Boundary-Value Problem for a Generalized Stokes System in a Half-Space

The paper contains the construction of a solution of the Cauchy–Dirichlet problem in the half-space for a family of systems of differential equations that includes a Stokes system. For this solution, coercive estimates in the Hölder spaces of functions are obtained. Bibliography: 12 titles.     

The Cauchy Problem for the System of Maxwell Equations

We consider the problem of analytic continuation of a solution to the system of Maxwell equations in a bounded spatial domain from data on part of the boundary of the domain. We construct an approximate solution to the problem using the Carleman matrix method.     

On the Well-Posedness of a Two-Point Boundary-Value Problem for a System with Pseudodifferential Operators

We investigate the problem of the well-posedness of a boundary-value problem for a system of pseudodifferential equations of arbitrary order with nonlocal conditions. The equation and boundary conditions contain pseudodifferential operators whose symbols are defined and continuous in a certain domain H ⊂ ℝ _σ ^m . A criterion for the existence and uniqueness of solutions and for the continuous dependence of the solution on the boundary function is established. __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 8, pp. 1131 – 1136, August, 2005.     

Two-Parameter Asymptotics in a Boundary-Value Problem for the Laplacian

We study a model boundary-value problem for the Laplacian in the unit disk with closely-spaced and periodic alternation of the type of boundary condition for the case in which the Dirichlet problem is the limit one. We study and justify the two-parameter asymptotics of an eigenvalue of the perturbed problem converging to a simple eigenvalue of the limit problem.     

非局部非对称弹性理论混合边值问题的提法

从完全的虚功和虚功率原理以及广义Ｐｉｏｌａ定理出发一并推导出非局部非对称弹性理论的运动方程、所有边界条件和全能量方程。把这时给出的边界条件和高键,戴天民的相应结果加在一超即可表述非局部非对称线性弹性理论的混合边值问题。     

L p -Estimates for Solutions to the Initial Boundary-Value Problem for the Generalized Stokes System in a Bounded Domain

The main result of the paper is the proof of the solvability in anisotropic Sobolev spaces. Bibliography: 23 titles.     

Quintic Spline Approach to the Solution of a Singularly-Perturbed Boundary-Value Problem

A fourth-order uniform mesh difference scheme using quintic splines for solving a singularly-perturbed boundary-value problem of the form

Hyperbolic Boundary-Value Problem for a Piecewise Homogeneous Hollow Cylinder

Ukrainian Mathematical Journal - By the method of integral and hybrid integral transforms in combination with the method of principal solutions (matrices of influence and Green matrices), we...     

On a Frankl-Type Boundary-Value Problem for a Mixed-Type Degenerating Equation

Ukrainian Mathematical Journal - We study the existence and uniqueness of solutions for an analog of the Frankl-type boundary-value problem for a parabolic-hyperbolic-type equation. The uniqueness...     

具有奇性的非线性椭圆方程的边值问题

本文研究奇异椭圆方程的边值问题.利用变分方法和锥理论中的混合单调方法,证明了奇异方程正解的存在性、唯一性.     

Solvability of a Three-Point Boundary-Value Problem for a Second-Order Differential Inclusion

We investigate the problem of the existence of solutions of a three-point boundary-value problem for a second order differential inclusion.     

The Second Boundary-Value Problem for Pseudoparabolic Equations in Noncylindrical Domains

This paper is devoted to the study of the solvability of the second mixed problem in a noncylindrical domain for the nonstationary equation $${\text{div}}(k(x){\text{ grad }}u_t ) - c(x)u_t - b(x)u(x,t) = f(x,t)$$ called the pseudoparabolic equation. We prove existence and uniqueness theorems for the solution in the case of contracting (as time t increases) domains.     

Boundary-Value Problem for Functional-Differential Advanced-Retarded Tricomi Equation

We investigate the boundary-value problem for Tricomi mixed-type equation with multiple functional retarding and advancing. We construct the general solution to the equation. The problem is uniquely solvable.     

A Stability Estimate for a Solution to a Three-Dimensional Inverse Problem for the Maxwell Equations

We consider the problem of determining dielectric permittivity and conductivity in the Maxwell equations. As additional information we prescribe the traces of the tangential components of the electromagnetic field on the lateral surface of a cylindric domain. We establish a stability estimate for a solution to the inverse problem and a uniqueness theorem.     

Multiplicity of Solutions to a Boundary-Value Problem with Nonlinear Neumann Condition

We consider the boundary-value problem

On a Two-Point Boundary-Value Problem with Spurious Solutions

The Carrier–Pearson equation     with boundary conditions   u (−1) = u (1) = 0  is studied from a rigorous point of view. Known solutions obtained from the method of matched asymptotics are shown to approximate true solutions within an exponentially small error estimate. The so-called spurious solutions turn out to be approximations of true solutions, when the locations of their "spikes" are properly assigned. An estimate is also given for the maximum number of spikes that these solutions can have.     

Approximate Synthesis of Optimal Bounded Control for a Parabolic Boundary-Value Problem

We consider the approximate optimal control based on the principle of feedback relation (synthesis) for a parabolic boundary-value problem. We represent the feedback operator as Fourier series in the eigenfunctions of the Laplace operator, which does not enable us to use these results in practice. In view of this fact, we justify the convergence of approximate controls, switching points, and values of the quality criterion to the exact values of the corresponding variables.