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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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030078
I. M. Tsvetkov
{"title":"On the Dynamic Tension of a Thin Round Perfectly Rigid-Plastic Layer Made of Transversely Isotropic Material","authors":"I. M. Tsvetkov","doi":"10.1134/s0012266124030078","DOIUrl":"https://doi.org/10.1134/s0012266124030078","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a system of equations modeling the dynamic tension of a homogeneous round\u0000layer of incompressible perfectly rigid-plastic transversely isotropic material obeying the\u0000Mises–Hencky criterion. The upper and lower bases are stress-free, the radial velocity is set on the\u0000lateral boundary, and the possibility of thickening or thinning of the layer, simulating formation\u0000and further development of a neck, is taken into account. Using the method of asymptotic\u0000integration, two characteristic tension modes are identified, that is, relations of dimensionless\u0000parameters are determined that necessitate taking into account inertial terms. An approximate\u0000solution of the problem is constructed when considering the mode associated with the acceleration\u0000on the lateral face reaching its critical values.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030017
I. S. Lomov
{"title":"Study of the Asymptotic Properties of the Solution to a Problem with a Parameter for the Sturm–Liouville Operator with a Singular Potential","authors":"I. S. Lomov","doi":"10.1134/s0012266124030017","DOIUrl":"https://doi.org/10.1134/s0012266124030017","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The Sturm–Liouville operator with a singular potential is defined on an interval of the real\u0000line. Transmission conditions are specified at an interior point of the interval. The operator\u0000potential may have a nonintegrable singularity. For the strong solution of the Cauchy problem for\u0000an equation with a parameter, asymptotic formulas and estimates are obtained on each of the\u0000solution smoothness intervals.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576707","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s001226612403008x
A. V. Podobryaev
{"title":"Sub-Lorentzian Extremals Defined by an Antinorm","authors":"A. V. Podobryaev","doi":"10.1134/s001226612403008x","DOIUrl":"https://doi.org/10.1134/s001226612403008x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a left-invariant sub-Lorentzian structure on a Lie group. This structure is\u0000assumed to be defined by a closed convex salient cone in the corresponding Lie algebra and a\u0000continuous antinorm associated with this cone. We derive the Hamiltonian system for\u0000sub-Lorentzian extremals and give conditions under which normal extremal trajectories keep their\u0000causal type. Tangent vectors of abnormal extremal trajectories are either lightlike or are tangent\u0000vectors of sub-Riemannian abnormal extremal trajectories for the sub-Riemannian distribution\u0000spanned by the cone.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030066
D. P. Emel’yanov
{"title":"Solution of a Boundary Value Problem for an Elliptic Equation with a Small Noninteger Order Degeneracy","authors":"D. P. Emel’yanov","doi":"10.1134/s0012266124030066","DOIUrl":"https://doi.org/10.1134/s0012266124030066","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the Dirichlet boundary value problem for an elliptic type equation with\u0000irregular noninteger-order degeneration in a rectangle. The coefficients of the differential operator\u0000are supposed to be analytic. We construct a formal solution by using the method of spectral\u0000separation of singularities in the form of a series; the character of the nonanalytic dependence of\u0000the solution on the variable <span>(y)</span> in a neighborhood of\u0000<span>(y=0 )</span> is written out explicitly. We prove the convergence\u0000of the series to the classical solution using the Green’s function method.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030029
A. E. Mamatov
{"title":"Direct Problem of Scattering Theory for a Dirac System of Differential Equations on the Half-Line in the Case of Finite Density","authors":"A. E. Mamatov","doi":"10.1134/s0012266124030029","DOIUrl":"https://doi.org/10.1134/s0012266124030029","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, we study the direct scattering problem on the half-line for the Dirac system\u0000of differential equations in the case of finite density with the boundary condition <span>(y_{1}(0)=y_{2}(0) )</span>. The spectrum is studied, the resolvent is\u0000constructed, and the spectral expansion in the eigenfunctions of the Dirac operator is obtained.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030030
E. Mukhamadiev, A. N. Naimov
{"title":"On the Solvability of a Periodic Problem for a System of Second-Order Nonlinear Ordinary Differential Equations","authors":"E. Mukhamadiev, A. N. Naimov","doi":"10.1134/s0012266124030030","DOIUrl":"https://doi.org/10.1134/s0012266124030030","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The solvability of a periodic problem for a system of nonlinear second-order ordinary\u0000differential equations with a positively homogeneous main part is investigated. New conditions are\u0000found that ensure an a priori estimate for the solutions of the periodic problem under\u0000consideration. The conditions are stated in terms of the properties of the positively homogeneous\u0000main part of the system. Under the a priori estimate, using and developing methods for calculating\u0000the mapping degree for vector fields, we prove a theorem on the solvability of the periodic problem\u0000that generalizes the results previously obtained by the present authors on the study of the periodic\u0000problem for systems of second-order nonlinear ordinary differential equations.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030108
V. M. Goloviznin, V. V. Konoplyanikov, P. A. Maiorov, S. I. Mukhin
{"title":"Balance-Characteristic Method for Calculating Hemodynamics of a Single Vessel","authors":"V. M. Goloviznin, V. V. Konoplyanikov, P. A. Maiorov, S. I. Mukhin","doi":"10.1134/s0012266124030108","DOIUrl":"https://doi.org/10.1134/s0012266124030108","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper is devoted to constructing a numerical algorithm for calculating the blood flow\u0000in a volume vessel. A system of differential equations describing the dynamics of fluid in a single\u0000vessel with moving walls in cylindrical coordinates is derived assuming axial symmetry in\u0000arbitrary Eulerian-Lagrangian variables. A balance-characteristic scheme based on the Cabaret\u0000methodology is constructed for the obtained system of equations. The results of calculations of\u0000test problems are given.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030054
A. V. Glushak
{"title":"On the Solvability of Initial and Boundary Value Problems for Abstract Functional-Differential Euler–Poisson–Darboux Equations","authors":"A. V. Glushak","doi":"10.1134/s0012266124030054","DOIUrl":"https://doi.org/10.1134/s0012266124030054","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In a Banach space, we consider the Cauchy problem and the Dirichlet and Neumann\u0000boundary value problems for a functional-differential equation generalizing the\u0000Euler–Poisson–Darboux equation. A sufficient condition for the solvability of the Cauchy problem\u0000is proved, and an explicit form of the resolving operator is indicated, which is written using the\u0000Bessel and Struve operator functions introduced by the author. For boundary value problems in\u0000the hyperbolic case, we establish conditions imposed on the operator coefficient of the equation\u0000and the boundary elements that are sufficient for the unique solvability of these problems.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030042
M. V. Shamolin
{"title":"Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom","authors":"M. V. Shamolin","doi":"10.1134/s0012266124030042","DOIUrl":"https://doi.org/10.1134/s0012266124030042","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Tensor invariants (first integrals and differential forms) of homogeneous dynamical systems\u0000on the tangent bundles of smooth three-dimensional manifolds (systems with three degrees of\u0000freedom) are presented in this paper. The connection between the presence of such invariants and\u0000the complete set of the first integrals needed for the integration of geodesic, potential, and\u0000dissipative systems is shown. At the same time, the force fields introduced make the systems in\u0000question dissipative with dissipation of different signs and generalize the previously considered\u0000ones.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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
Differential Equations Pub Date : 2024-07-08 DOI: 10.1134/s0012266124030091
A. V. Chernov
{"title":"On the Exact Global Controllability of a Semilinear Evolution Equation","authors":"A. V. Chernov","doi":"10.1134/s0012266124030091","DOIUrl":"https://doi.org/10.1134/s0012266124030091","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For the Cauchy problem associated with a controlled semilinear evolution equation with\u0000an operator (not necessarily bounded) in a Hilbert space, we obtain sufficient conditions for exact\u0000controllability into a given terminal state (and also into given intermediate states at interim time\u0000moments) on an arbitrarily fixed (without additional constraints) time interval. Here we use the\u0000Browder—Minty theorem and also a chain technology of successive continuation of the solution of\u0000the controlled system to intermediate states. As examples, we consider a semilinear\u0000pseudoparabolic equation and a semilinear wave equation.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141576831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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