Pub Date : 2024-04-09DOI: 10.26907/0021-3446-2024-3-84-90
S. K. Vodopyanov, D. A. Sboev
In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.
{"title":"Lower semicontinuity of distortion coefficients for homeomorphisms of bounded (1, sigma )-weighted (q, p)-distortion on Carnot groups","authors":"S. K. Vodopyanov, D. A. Sboev","doi":"10.26907/0021-3446-2024-3-84-90","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-84-90","url":null,"abstract":"In this paper we study the locally uniform convergence of homeomorphisms with bounded (1,σ)-weighted (q,p)-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded (1,σ)-weighted (q,p)-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"23 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140722000","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}
Pub Date : 2024-04-09DOI: 10.26907/0021-3446-2024-3-64-69
V. B. Levenshtam
A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semi-axis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semi-axis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov-Bogolyubov averaging method on the semi-axis is justified.
{"title":"Averaging of a normal system of ordinary differential equations of high frequency with a multipoint boundary value problem on a semi-axis","authors":"V. B. Levenshtam","doi":"10.26907/0021-3446-2024-3-64-69","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-64-69","url":null,"abstract":"A multipoint boundary value problem for a nonlinear normal system of ordinary differential equations with a rapidly time-oscillating right-hand side is considered on a positive time semi-axis. For this problem, which depends on a large parameter (high oscillation frequency), a limiting (averaged) multipoint boundary value problem is constructed and a limiting transition in the Hölder space of bounded vector functions defined on the considered semi-axis is justified. Thus, for normal systems of differential equations in the case of a multipoint boundary value problem, the Krylov-Bogolyubov averaging method on the semi-axis is justified.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"31 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140720693","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}
Pub Date : 2024-04-08DOI: 10.26907/0021-3446-2024-3-50-63
V. I. Korzyuk, J. V. Rudzko
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 of some integral equation. The local solvability of this equation 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.
{"title":"Classical solution of the Cauchy problem for a semilinear hyperbolic equation in the case of two independent variables","authors":"V. I. Korzyuk, J. V. Rudzko","doi":"10.26907/0021-3446-2024-3-50-63","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-50-63","url":null,"abstract":"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 of some integral equation. The local solvability of this equation 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.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"282 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140730278","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}
Pub Date : 2024-04-08DOI: 10.26907/0021-3446-2024-3-15-37
M. Y. Vatolkin
{"title":"Investigation of the asymptotics of the eigenvalues of a second order quasidifferential boundary value problem","authors":"M. Y. Vatolkin","doi":"10.26907/0021-3446-2024-3-15-37","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-15-37","url":null,"abstract":"","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"29 28","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140732302","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}
Pub Date : 2024-04-08DOI: 10.26907/0021-3446-2024-3-38-49
D. Durdiev
In this paper, we study the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, the Tricomi problem for this equation with a non-characteristic line of type change is considered. The unknown of the inverse problem is the variable coefficient at the lowest derivative in the parabolic equation. To determine it, two inverse problems are studied: with respect to the solution defined in the parabolic part of the domain, the integral overdetermination condition (inverse problem 1) and one simple observation at a fixed point (inverse problem 2) are given. Theorems on the unique solvability of the formulated problems in the sense of classical solution are proved.
{"title":"Coefficient inverse problem for an equation of mixed parabolic-hyperbolic type with a non-characteristic line of type change","authors":"D. Durdiev","doi":"10.26907/0021-3446-2024-3-38-49","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-38-49","url":null,"abstract":"In this paper, we study the direct and two inverse problems for a model equation of mixed parabolic-hyperbolic type. In the direct problem, the Tricomi problem for this equation with a non-characteristic line of type change is considered. The unknown of the inverse problem is the variable coefficient at the lowest derivative in the parabolic equation. To determine it, two inverse problems are studied: with respect to the solution defined in the parabolic part of the domain, the integral overdetermination condition (inverse problem 1) and one simple observation at a fixed point (inverse problem 2) are given. Theorems on the unique solvability of the formulated problems in the sense of classical solution are proved.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"99 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140731749","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}
Pub Date : 2024-04-08DOI: 10.26907/0021-3446-2024-3-3-14
N. Agafonova, S. Volosivets
We give some necessary and sufficient conditions 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 Cv .V. Stanojevi´c and extend some results of F. M´oricz proved for Walsh–Fourier series
我们给出了关于乘法系统和相应傅里叶级数的级数和的广义导数收敛的一些必要和充分条件。这些条件与 S. Sheng、W.O. Bray 和 Cv .V. Stanojevi´c 的三角函数结果相对应，并扩展了 F. M´oricz 为沃尔什-傅里叶级数证明的一些结果。
{"title":"Integrability of series with respect to multiplicative systems and generalized derivatives","authors":"N. Agafonova, S. Volosivets","doi":"10.26907/0021-3446-2024-3-3-14","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-3-3-14","url":null,"abstract":"We give some necessary and sufficient conditions 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 Cv .V. Stanojevi´c and extend some results of F. M´oricz proved for Walsh–Fourier series","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"179 S443","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140731078","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}
Pub Date : 2024-03-13DOI: 10.26907/0021-3446-2024-2-85-90
M. I. Muminov, I. Bozorov, T. Rasulov
In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σess(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σess(H) are singled out. We prove that the essential spectrum σess(H) consists of no more than six segments (components).
本文将 2х2 块算子矩阵 H 视为希尔伯特空间中的有界自关节算子。通过广义弗里德里希模型的谱来描述算子矩阵 H 的本质σess(H) 的位置，即本质谱 σess(H)的两粒子和三粒子分支。我们证明了本质谱 σess(H) 由不超过六个分段（成分）组成。
{"title":"On the number of components of the essential spectrum of one 2х2 operator matrix","authors":"M. I. Muminov, I. Bozorov, T. Rasulov","doi":"10.26907/0021-3446-2024-2-85-90","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-2-85-90","url":null,"abstract":"In this paper, a 2х2 block operator matrix H is considered as a bounded and self-adjointoperator in a Hilbert space. The location of the essential σess(H) of operator matrix H is described via the spectrum of the generalized Friedrichs model, i.e. the two- and three-particle branches of the essential spectrum σess(H) are singled out. We prove that the essential spectrum σess(H) consists of no more than six segments (components).","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"408 2‐3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140246884","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}
Pub Date : 2024-03-13DOI: 10.26907/0021-3446-2024-2-91-99
V. N. Paimushin, A. N. Nuriev, S. F. Chumakova
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 (rigid connection) 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 shear model of S.P. Timoshenko, compiled for rods in a geometrically nonlinear approximation without taking into account lateral strain deformations. For the section fastened on the elastic support element, a one-dimensional shear deformation model is constructed taking into account lateral strain deformations, 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 force conditions for the coupling 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
{"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":"10.26907/0021-3446-2024-2-91-99","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-2-91-99","url":null,"abstract":" 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 (rigid connection) 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 shear model of S.P. Timoshenko, compiled for rods in a geometrically nonlinear approximation without taking into account lateral strain deformations. For the section fastened on the elastic support element, a one-dimensional shear deformation model is constructed taking into account lateral strain deformations, 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 force conditions for the coupling 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","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"269 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140247323","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}
Pub Date : 2024-03-11DOI: 10.26907/0021-3446-2024-2-37-58
R. Kumar, S. Kaushal, Bh. Pragati
In the present study, we explore a new mathematical formulation involving modifiedcouple stress thermoelastic diffusion (MCTD) with nonlocal, voids and phase lags. The governingequations are expressed in dimensionless form for the further investigation. The desired equationsare expressed in terms of elementary functions by assuming time harmonic variation of the fieldvariables (displacement, temperature field, chemical potential and volume fraction field). Thefundamental 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 beenexamined for two dimensional cases. The characteristic equation yields the attributes of waves likephase velocity, attenuation coefficients, specific loss and penetration depth which are computednumerically and presented in form of distinct graphs. Some unique cases are also deduced. Theresults provide the motivation for the researcher to investigate thermally conducted modified couplestress elastic material under nonlocal, porosity and phase lags impacts as a new class of applicablematerials.
{"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, Bh. Pragati","doi":"10.26907/0021-3446-2024-2-37-58","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-2-37-58","url":null,"abstract":"In the present study, we explore a new mathematical formulation involving modifiedcouple stress thermoelastic diffusion (MCTD) with nonlocal, voids and phase lags. The governingequations are expressed in dimensionless form for the further investigation. The desired equationsare expressed in terms of elementary functions by assuming time harmonic variation of the fieldvariables (displacement, temperature field, chemical potential and volume fraction field). Thefundamental 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 beenexamined for two dimensional cases. The characteristic equation yields the attributes of waves likephase velocity, attenuation coefficients, specific loss and penetration depth which are computednumerically and presented in form of distinct graphs. Some unique cases are also deduced. Theresults provide the motivation for the researcher to investigate thermally conducted modified couplestress elastic material under nonlocal, porosity and phase lags impacts as a new class of applicablematerials.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140254446","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}
Pub Date : 2024-03-11DOI: 10.26907/0021-3446-2024-2-3-21
O. V. Glazyrina, R. Dautov, D. A. Gubaidullina
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.
{"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. Dautov, D. A. Gubaidullina","doi":"10.26907/0021-3446-2024-2-3-21","DOIUrl":"https://doi.org/10.26907/0021-3446-2024-2-3-21","url":null,"abstract":" 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.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"11 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140254063","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}
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