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Classical Solution to the Cauchy Problem for a Semilinear Hyperbolic Equation in the Case of Two Independent Variables 两个独立变量情况下半线性双曲方程考希问题的经典解法
IF 0.4
Russian Mathematics Pub Date : 2024-06-25 DOI: 10.3103/s1066369x24700178
V. I. Korzyuk, J. V. Rudzko
{"title":"Classical Solution to the Cauchy Problem for a Semilinear Hyperbolic Equation in the Case of Two Independent Variables","authors":"V. I. Korzyuk, J. V. Rudzko","doi":"10.3103/s1066369x24700178","DOIUrl":"https://doi.org/10.3103/s1066369x24700178","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the upper half-plane, we consider a semilinear hyperbolic partial differential equation of order higher than two. The operator in the equation is a composition of first-order differential operators. The equation is accompanied with Cauchy conditions. The solution is constructed in an implicit analytical form as a solution to some integral equation. The local solvability of this euqation is proved by the Banach fixed point theorem and/or the Schauder fixed point theorem. The global solvability of this equation is proved by the Leray–Schauder fixed point theorem. For the problem in question, the uniqueness of the solution is proved and the conditions under which its classical solution exists are established.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Spectral Relations for a Matrix Model in Fermionic Fock Space 费米子 Fock 空间矩阵模型的谱关系
IF 0.4
Russian Mathematics Pub Date : 2024-06-25 DOI: 10.3103/s1066369x2470021x
T. Kh. Rasulov, D. E. Ismoilova
{"title":"Spectral Relations for a Matrix Model in Fermionic Fock Space","authors":"T. Kh. Rasulov, D. E. Ismoilova","doi":"10.3103/s1066369x2470021x","DOIUrl":"https://doi.org/10.3103/s1066369x2470021x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A matrix model <span>(mathcal{A})</span> is considered related to a system describing two identical fermions and one particle of another nature on a lattice, interacting via annihilation and creation operators. The problem of the study of the spectrum of a block operator matrix <span>(mathcal{A})</span> is reduced to the investigation of the spectrum of block operator matrices of order three with a discrete variable, and the relations for the spectrum, essential spectrum, and point spectrum are established. Two-particle and three-particle branches of the essential spectrum of the block operator matrix <span>(mathcal{A})</span> are singled out.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integrability of Series with Respect to Multiplicative Systems and Generalized Derivatives 关于乘法系统和广义衍生数列的可积分性
IF 0.4
Russian Mathematics Pub Date : 2024-06-25 DOI: 10.3103/s1066369x24700142
N. Yu. Agafonova, S. S. Volosivets
{"title":"Integrability of Series with Respect to Multiplicative Systems and Generalized Derivatives","authors":"N. Yu. Agafonova, S. S. Volosivets","doi":"10.3103/s1066369x24700142","DOIUrl":"https://doi.org/10.3103/s1066369x24700142","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We give some necessary and sufficient conditiosn for the convergence of generalized derivatives of sums of series with respect to multiplicative systems and the corresponding Fourier series. These conditions are counterparts of trigonometric results of S. Sheng, W.O. Bray, and Č.V. Stanojević and extend some results of F. Móricz proved for Walsh–Fourier series.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wave Analysis and Representation of Fundamental Solution in Modified Couple Stress Thermoelastic Diffusion with Voids, Nonlocal and Phase Lags 有空隙、非局部和相位滞后的修正耦合应力热弹性扩散中的波分析和基本解的表示方法
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700099
R. Kumar, S. Kaushal, Pragati
{"title":"Wave Analysis and Representation of Fundamental Solution in Modified Couple Stress Thermoelastic Diffusion with Voids, Nonlocal and Phase Lags","authors":"R. Kumar, S. Kaushal, Pragati","doi":"10.3103/s1066369x24700099","DOIUrl":"https://doi.org/10.3103/s1066369x24700099","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In the present study, we explored a new mathematical formulation involving modified couple stress thermoelastic diffusion (MCTD) with nonlocal, voids and phase lags. The governing equations are expressed in dimensionless form for the further investigating. The desired equations are expressed in terms of elementary functions by assuming time harmonic variation of the field variables (displacement, temperature field, chemical potential and volume fraction field). The fundamental solutions are constructed for the obtained system of equations for steady oscillation and some basic features of the solutions are established. Also, plane wave vibrations has been examined for two dimensional cases. The characteristic equation yields the attributes of waves like phase velocity, attenuation coefficients, specific loss and penetration depth which are computed numerically and presented in form of distinct graphs. Some unique cases are also deduced. The results provide the motivation for the researcher to investigate thermally conducted modified couple stress elastic material under nonlocal, porosity and phase lags impacts as a new class of applicable materials.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Number of Components of the Essential Spectrum of One 2 × 2 Operator Matrix 论一个 2 × 2 算子矩阵的基本频谱成分数
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700129
M. I. Muminov, I. N. Bozorov, T. Kh. Rasulov
{"title":"On the Number of Components of the Essential Spectrum of One 2 × 2 Operator Matrix","authors":"M. I. Muminov, I. N. Bozorov, T. Kh. Rasulov","doi":"10.3103/s1066369x24700129","DOIUrl":"https://doi.org/10.3103/s1066369x24700129","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, a <span>(2 times 2)</span> block operator matrix <span>(H)</span> is considered as a bounded and self-adjoint operator in a Hilbert space. The location of the essential spectrum <span>({{sigma }_{{{text{ess}}}}}(H))</span> of operator matrix <span>(H)</span> is described via the spectrum of the generalized Friedrichs model, i.e., the two- and three-particle branches of the essential spectrum <span>({{sigma }_{{{text{ess}}}}}(H))</span> are singled out. We prove that the essential spectrum <span>({{sigma }_{{{text{ess}}}}}(H))</span> consists of no more than six segments (components).</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Transformation Model of the Dynamic Deformation of an Elongated Cantilever Plate Mounted on an Elastic Support Element 安装在弹性支撑元件上的伸长悬臂板动态变形的变换模型
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700130
V. N. Paimushin, A. N. Nuriev, S. F. Chumakova
{"title":"Transformation Model of the Dynamic Deformation of an Elongated Cantilever Plate Mounted on an Elastic Support Element","authors":"V. N. Paimushin, A. N. Nuriev, S. F. Chumakova","doi":"10.3103/s1066369x24700130","DOIUrl":"https://doi.org/10.3103/s1066369x24700130","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A transformation model of the dynamic deformation of an elongated orthotropic composite rod-type plate, consisting of two sections (fastened and free) along its length, is proposed. In the free section, the orthotropic axes of the material do not coincide with the axes of the Cartesian coordinate system chosen for the plate, and in the fastened section, the displacements of points of the contact’s boundary surface (clamping) with the elastic support element are considered to be known. The constructed model is based on the use for the free section of the relations of the refined Timoshenko shear model, compiled for rods in a geometrically nonlinear approximation without taking into account lateral contraction. For the section fastened on the elastic support element, a one-dimensional shear deformation model is built taking into account lateral contraction, which is transformed into another model by satisfying the conditions of kinematic coupling with the elastic support element with given displacements of the interface points with the plate. The conditions for the kinematic coupling of the free and fastened sections of the plate are formulated. Based on the Hamilton–Ostrogradsky variational principle, the corresponding equations of motion and boundary conditions, as well as the static conditions for the matching of sections, are derived. The constructed model is intended to simulate natural processes and structures when solving applied engineering problems aimed at developing innovative oscillatory biomimetic propulsors.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141257244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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 Classification of Points of a Unit Circle for Subharmonic Functions of the Class $$mathfrak{A}{kern 1pt} text{*}$$ 论$$mathfrak{A}{/kern 1pt} 类次谐函数单位圆上点的分类text{*}$$
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700117
S. L. Berberyan
{"title":"On the Classification of Points of a Unit Circle for Subharmonic Functions of the Class $$mathfrak{A}{kern 1pt} text{*}$$","authors":"S. L. Berberyan","doi":"10.3103/s1066369x24700117","DOIUrl":"https://doi.org/10.3103/s1066369x24700117","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A class <span>(mathfrak{A}{kern 1pt} text{*})</span> consisting of subharmonic functions in the unit disk such that their superpositions with some families of linear fractional automorphisms of the disk form normal families is considered. A theorem stating that for any function of class <span>(mathfrak{A}{kern 1pt} text{*})</span> the set of points of the unit circle can be represented as a union of a set of Fatou points, a set of generalized Plesner points, and a set of measure zero is proved.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Quasi-Invariance of Harmonic Measure and Hayman–Wu Theorem 论谐波量的准不变量和海曼-吴定理
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700087
S. Yu. Graf
{"title":"On Quasi-Invariance of Harmonic Measure and Hayman–Wu Theorem","authors":"S. Yu. Graf","doi":"10.3103/s1066369x24700087","DOIUrl":"https://doi.org/10.3103/s1066369x24700087","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This study defines and describes the properties of the class of diffeomorphisms of the unit disk <span>(mathbb{D} = { z,:;|{kern 1pt} z{kern 1pt} |; &lt; 1} )</span> on the complex plane <span>(mathbb{C})</span> for which the harmonic measure of the boundary arcs of the slit disk has a limited distortion (i.e., is quasi-invariant). Estimates for derivative mappings of this class are obtained. We prove that such mappings are quasiconformal and quasi-isometries with respect to the pseudohyperbolic metric. An example of a mapping with the specified property is given. As an application, a generalization of the Hayman–Wu theorem to this class of such mappings is proved.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $$mathbb{A}{{mathbb{T}}_{{lambda ,j}}}$$ 论使用算子 $$mathbb{A}{{mathbb{T}}_{{lambda ,j}} 求解抛物型方程混合边界值问题的一种方法
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700105
A. Yu. Trynin
{"title":"On One Method for Solving a Mixed Boundary Value Problem for a Parabolic Type Equation Using Operators $$mathbb{A}{{mathbb{T}}_{{lambda ,j}}}$$","authors":"A. Yu. Trynin","doi":"10.3103/s1066369x24700105","DOIUrl":"https://doi.org/10.3103/s1066369x24700105","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper proposes a new method for obtaining a generalized solution to the mixed boundary value problem for a parabolic equation with boundary conditions of the third kind and a continuous initial condition. Generalized functions are understood in the sense of the sequential approach. The representative of the class of sequences, which is a generalized function, is obtained using the function interpolation operator, constructed using solutions to the Cauchy problem. The solution is obtained in the form of a series that converges uniformly inside the domain of the solution.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254550","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Accuracy of an Implicit Scheme for the Finite Element Method with a Penalty for a Nonlocal Parabolic Obstacle Problem 非局部抛物线障碍问题中带有惩罚的有限元法隐含方案的精度
IF 0.4
Russian Mathematics Pub Date : 2024-06-04 DOI: 10.3103/s1066369x24700075
O. V. Glazyrina, R. Z. Dautov, D. A. Gubaidullina
{"title":"Accuracy of an Implicit Scheme for the Finite Element Method with a Penalty for a Nonlocal Parabolic Obstacle Problem","authors":"O. V. Glazyrina, R. Z. Dautov, D. A. Gubaidullina","doi":"10.3103/s1066369x24700075","DOIUrl":"https://doi.org/10.3103/s1066369x24700075","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In order to solve a parabolic variational inequality with a nonlocal spatial operator and a one-sided constraint on the solution, a numerical method based on the penalty method, finite elements, and the implicit Euler scheme is proposed and studied. Optimal estimates for the accuracy of the approximate solution in the energy norm are obtained.</p>","PeriodicalId":46110,"journal":{"name":"Russian Mathematics","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141254663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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