Differential Equations最新文献

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On the Dynamic Tension of a Thin Round Perfectly Rigid-Plastic Layer Made of Transversely Isotropic Material 论横向各向同性材料薄圆完全刚塑层的动态张力

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030078

I. M. Tsvetkov

Abstract

We study a system of equations modeling the dynamic tension of a homogeneous roundlayer of incompressible perfectly rigid-plastic transversely isotropic material obeying theMises–Hencky criterion. The upper and lower bases are stress-free, the radial velocity is set on thelateral boundary, and the possibility of thickening or thinning of the layer, simulating formationand further development of a neck, is taken into account. Using the method of asymptoticintegration, two characteristic tension modes are identified, that is, relations of dimensionlessparameters are determined that necessitate taking into account inertial terms. An approximatesolution of the problem is constructed when considering the mode associated with the accelerationon the lateral face reaching its critical values.

摘要我们研究了一个方程组，该方程组模拟了服从米塞斯-亨茨基准则的不可压缩完全刚塑横向各向同性材料均匀圆层的动态张力。上下基面无应力，径向速度设置在侧边界上，并考虑了层增厚或减薄的可能性，模拟了颈部的形成和进一步发展。利用渐近积分法确定了两种特征张力模式，即确定了需要考虑惯性项的无量纲参数关系。在考虑与侧面加速度达到临界值相关的模式时，构建了问题的近似解决方案。

引用次数: 0

Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential 具有奇异势的 Sturm-Liouville 算子带参数问题解的渐近特性研究

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030017

I. S. Lomov

Abstract

The Sturm–Liouville operator with a singular potential is defined on an interval of the realline. Transmission conditions are specified at an interior point of the interval. The operatorpotential may have a nonintegrable singularity. For the strong solution of the Cauchy problem foran equation with a parameter, asymptotic formulas and estimates are obtained on each of thesolution smoothness intervals.

摘要带奇异势的 Sturm-Liouville 算子定义在一个重线段上。在区间的内点规定了传递条件。算子势可能具有不可解奇点。对于带参数方程的考希问题的强解，在每个解的平滑区间上都得到了渐近公式和估计值。

引用次数: 0

Sub-Lorentzian Extremals Defined by an Antinorm 反规范定义的次洛伦兹极值

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s001226612403008x

A. V. Podobryaev

Abstract

We consider a left-invariant sub-Lorentzian structure on a Lie group. This structure isassumed to be defined by a closed convex salient cone in the corresponding Lie algebra and acontinuous antinorm associated with this cone. We derive the Hamiltonian system forsub-Lorentzian extremals and give conditions under which normal extremal trajectories keep theircausal type. Tangent vectors of abnormal extremal trajectories are either lightlike or are tangentvectors of sub-Riemannian abnormal extremal trajectories for the sub-Riemannian distributionspanned by the cone.

摘要我们考虑了在一个李群上的左不变亚洛伦兹结构。该结构被假定为由相应的李代数中的闭凸突出锥和与该锥相关的连续反规范所定义。我们推导了次洛伦兹极值的哈密顿系统，并给出了正常极值轨迹保持其因果类型的条件。异常极值轨迹的切向量要么是轻型的，要么是锥体所扫描的亚黎曼分布的亚黎曼异常极值轨迹的切向量。

引用次数: 0

Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy 小非整数阶畸变椭圆方程的边界值问题求解

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030066

D. P. Emel’yanov

Abstract

We consider the Dirichlet boundary value problem for an elliptic type equation withirregular noninteger-order degeneration in a rectangle. The coefficients of the differential operatorare supposed to be analytic. We construct a formal solution by using the method of spectralseparation of singularities in the form of a series; the character of the nonanalytic dependence ofthe solution on the variable (y) in a neighborhood of(y=0 ) is written out explicitly. We prove the convergenceof the series to the classical solution using the Green’s function method.

摘要我们考虑了矩形内不规则非整阶退化椭圆方程的 Dirichlet 边界值问题。微分算子的系数应该是解析的。我们利用奇点谱分离的方法，以数列的形式构造了一个正式的解；解在（y=0 ）附近对变量（y）的非解析依赖性的特征被明确写出。我们用格林函数法证明了数列对经典解的收敛性。

引用次数: 0

Direct Problem of Scattering Theory for a Dirac System of Differential Equations on the Half-Line in the Case of Finite Density 有限密度情况下半线上狄拉克微分方程系统的直接散射理论问题

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030029

A. E. Mamatov

Abstract

In this paper, we study the direct scattering problem on the half-line for the Dirac systemof differential equations in the case of finite density with the boundary condition (y_{1}(0)=y_{2}(0) ). The spectrum is studied, the resolvent isconstructed, and the spectral expansion in the eigenfunctions of the Dirac operator is obtained.

摘要本文研究了在有限密度情况下，边界条件为 (y_{1}(0)=y_{2}(0) )的狄拉克微分方程系统在半线上的直接散射问题。研究了频谱，构建了解析力，并得到了狄拉克算子特征函数的频谱展开。

引用次数: 0

On the Solvability of a Periodic Problem for a System of Second-Order Nonlinear Ordinary Differential Equations 论二阶非线性常微分方程系统周期问题的可解性

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030030

E. Mukhamadiev, A. N. Naimov

Abstract

The solvability of a periodic problem for a system of nonlinear second-order ordinarydifferential equations with a positively homogeneous main part is investigated. New conditions arefound that ensure an a priori estimate for the solutions of the periodic problem underconsideration. The conditions are stated in terms of the properties of the positively homogeneousmain part of the system. Under the a priori estimate, using and developing methods for calculatingthe mapping degree for vector fields, we prove a theorem on the solvability of the periodic problemthat generalizes the results previously obtained by the present authors on the study of the periodicproblem for systems of second-order nonlinear ordinary differential equations.

摘要研究了具有正均质主要部分的非线性二阶常微分方程系统的周期问题的可解性。研究发现了新的条件，这些条件可确保对所考虑的周期性问题的解进行先验估计。这些条件是根据系统正均质主部的性质提出的。在先验估计条件下，利用并发展了计算向量场映射度的方法，我们证明了周期问题的可解性定理，该定理概括了本文作者之前在二阶非线性常微分方程系统的周期问题研究中获得的结果。

引用次数: 0

Balance-Characteristic Method for Calculating Hemodynamics of a Single Vessel 计算单个血管血液动力学的平衡特性法

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030108

V. M. Goloviznin, V. V. Konoplyanikov, P. A. Maiorov, S. I. Mukhin

Abstract

The paper is devoted to constructing a numerical algorithm for calculating the blood flowin a volume vessel. A system of differential equations describing the dynamics of fluid in a singlevessel with moving walls in cylindrical coordinates is derived assuming axial symmetry inarbitrary Eulerian-Lagrangian variables. A balance-characteristic scheme based on the Cabaretmethodology is constructed for the obtained system of equations. The results of calculations oftest problems are given.

摘要本文致力于构建一种计算容积血管内血流的数值算法。在任意欧拉-拉格朗日变量的轴对称假设下，推导出了一个描述圆柱坐标下带移动壁的单容器中流体动力学的微分方程系。根据卡巴雷特方法，为得到的方程组构建了一个平衡特征方案。给出了测试问题的计算结果。

引用次数: 0

On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations 论抽象函数微分欧拉-泊松-达布方程的初值和边界问题的可解性

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030054

A. V. Glushak

Abstract

In a Banach space, we consider the Cauchy problem and the Dirichlet and Neumannboundary value problems for a functional-differential equation generalizing theEuler–Poisson–Darboux equation. A sufficient condition for the solvability of the Cauchy problemis proved, and an explicit form of the resolving operator is indicated, which is written using theBessel and Struve operator functions introduced by the author. For boundary value problems inthe hyperbolic case, we establish conditions imposed on the operator coefficient of the equationand the boundary elements that are sufficient for the unique solvability of these problems.

摘要在巴拿赫空间中，我们考虑了泛化欧拉-泊松-达尔布方程的函数微分方程的考希问题和狄利克特与诺伊曼边界值问题。证明了 Cauchy 问题可解性的充分条件，并指出了解析算子的明确形式，该形式是用作者引入的贝塞尔和斯特鲁夫算子函数写成的。对于双曲情况下的边界值问题，我们建立了施加于方程的算子系数和边界元素的条件，这些条件足以保证这些问题的唯一可解性。

引用次数: 0

Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom 具有三个自由度的大地、势和耗散系统的不变式

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030042

M. V. Shamolin

Abstract

Tensor invariants (first integrals and differential forms) of homogeneous dynamical systemson the tangent bundles of smooth three-dimensional manifolds (systems with three degrees offreedom) are presented in this paper. The connection between the presence of such invariants andthe complete set of the first integrals needed for the integration of geodesic, potential, anddissipative systems is shown. At the same time, the force fields introduced make the systems inquestion dissipative with dissipation of different signs and generalize the previously consideredones.

摘要本文介绍了光滑三维流形切线束上的均相动力系统（具有三个自由度的系统）的张量不变量（第一积分和微分形式）。本文说明了这些不变量的存在与测地、势和耗散系统积分所需的全套第一次积分之间的联系。同时，引入的力场使问题中的系统具有不同符号的耗散，并对之前考虑的系统进行了扩展。

引用次数: 0

On the Exact Global Controllability of a Semilinear Evolution Equation 论半线性演化方程的精确全局可控性

IF 0.6 4区数学 Q2 MATHEMATICS

Differential Equations

Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030091

A. V. Chernov

Abstract

For the Cauchy problem associated with a controlled semilinear evolution equation withan operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exactcontrollability into a given terminal state (and also into given intermediate states at interim timemoments) on an arbitrarily fixed (without additional constraints) time interval. Here we use theBrowder—Minty theorem and also a chain technology of successive continuation of the solution ofthe controlled system to intermediate states. As examples, we consider a semilinearpseudoparabolic equation and a semilinear wave equation.

摘要对于与希尔伯特空间中带有算子（不一定是有界的）的受控半线性演化方程相关的考奇问题，我们获得了在任意固定（无附加约束）时间间隔上精确可控性进入给定终态（以及在中间时刻进入给定中间状态）的充分条件。在这里，我们使用了布劳德-明蒂定理（Browder-Minty theorem），以及受控系统解连续延续到中间状态的链式技术。作为示例，我们考虑了一个半线性假抛物方程和一个半线性波方程。

引用次数: 0

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