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Contemporary Mathematics. Fundamental Directions最新文献

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Exceptional sets 特殊的集
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.1016/b978-0-12-334802-9.50009-2
A. S. Krivosheev, O. Krivosheeva
{"title":"Exceptional sets","authors":"A. S. Krivosheev, O. Krivosheeva","doi":"10.1016/b978-0-12-334802-9.50009-2","DOIUrl":"https://doi.org/10.1016/b978-0-12-334802-9.50009-2","url":null,"abstract":"","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134168521","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: 2
A family of piecewise-smooth solutions of a class of spatially distributed equations 一类空间分布方程的一组分段光滑解
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-06-30 DOI: 10.22363/2413-3639-2023-69-2-263-275
S. Kaschenko, D. S. Kosterin, S. Glyzin
{"title":"A family of piecewise-smooth solutions of a class of spatially distributed equations","authors":"S. Kaschenko, D. S. Kosterin, S. Glyzin","doi":"10.22363/2413-3639-2023-69-2-263-275","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-2-263-275","url":null,"abstract":"In this paper, we consider a spatially distributed equation with a periodic boundary condition and the zero integral mean condition in the spatial variable. The boundary-value problem under consideration has a family of solutions that are piecewise constant with respect to the spatial variable and have one discontinuity point. Conditions for the stability of such solutions are determined. The existence of piecewise constant solutions with more than one discontinuity point is shown. An algorithm for calculating solutions to a boundary-value problem by numerical methods is presented. A numerical analysis of the dynamics of the boundary-value problem is performed.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122078146","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 properties of operators in the problem on normal oscillations of a mixture of viscous compressible fluids 粘性可压缩流体正振问题中算符的谱性质
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-73-97
D. Zakora
{"title":"Spectral properties of operators in the problem on normal oscillations of a mixture of viscous compressible fluids","authors":"D. Zakora","doi":"10.22363/2413-3639-2023-69-1-73-97","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-73-97","url":null,"abstract":"In this paper, we study a problem of normal oscillations of a homogeneous mixture of several viscous compressible fluids filling a bounded domain of three-dimensional space with an infinitely smooth boundary. Two boundary conditions are considered: the no-slip condition and the slip condition without shear stresses. It is proved that the essential spectrum of the problem in both cases is a finite set of segments located on the real axis. The discrete spectrum lies on the real axis, except perhaps for a finite number of complex conjugate eigenvalues. The spectrum of the problem contains a subsequence of eigenvalues with a limit point at infinity and a power-law asymptotic distribution.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129210876","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
Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. Solvability and regularity problems 具有非对角主矩阵和强非线性梯度的拟线性椭圆型和抛物型系统。可解性和规律性问题
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-18-31
A. Arkhipova
{"title":"Quasilinear elliptic and parabolic systems with nondiagonal principal matrices and strong nonlinearities in the gradient. Solvability and regularity problems","authors":"A. Arkhipova","doi":"10.22363/2413-3639-2023-69-1-18-31","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-18-31","url":null,"abstract":"We consider nondiagonal elliptic and parabolic systems of equations with strongly nonlinear terms in the gradient. We review and comment known solvability and regularity results and describe the last author’s results in this field.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133171199","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: 1
Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak-Orlicz spaces Musielak-Orlicz空间中非线性椭圆型问题的熵与重整解
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-98-115
L. M. Kozhevnikova
{"title":"Entropy and renormalized solutions for a nonlinear elliptic problem in Musielak-Orlicz spaces","authors":"L. M. Kozhevnikova","doi":"10.22363/2413-3639-2023-69-1-98-115","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-98-115","url":null,"abstract":"In this paper, we establish the equivalence of entropy and renormalized solutions of second-order elliptic equations with nonlinearities defined by the Musielak-Orlicz functions and the right-hand side from the space L1(Ω). In nonreflexive Musielak-Orlicz-Sobolev spaces, we prove the existence and uniqueness of both entropy and renormalized solutions of the Dirichlet problem in domains with a Lipschitz boundary.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"233 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113985217","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
Integro-differential equations in Banach spaces and analytic resolving families of operators Banach空间中的积分-微分方程及算子族解析解
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-166-184
V. Fedorov, A. D. Godova
{"title":"Integro-differential equations in Banach spaces and analytic resolving families of operators","authors":"V. Fedorov, A. D. Godova","doi":"10.22363/2413-3639-2023-69-1-166-184","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-166-184","url":null,"abstract":"We study a class of equations in Banach spaces with a Riemann–Liouville-type integro-differential operator with an operator-valued convolution kernel. The properties of (k)-resolving operators of such equations are studied and the class (mathcal \u0000A_{m,K,chi}) of linear closed operators is defined such that the belonging to this class is necessary and, in the case of commutation of the operator with the convolution kernel, is sufficient for the existence of analytic in the sector (k)-resolving families of operators of the equation under study. Under certain additional conditions on the convolution kernel, we prove theorems on the unique solvability of the nonhomogeneous linear equation of the class under consideration if the nonhomogeneity is continuous in the norm of the graph of the operator from the equation or Hölder continuous. We obtain the theorem on sufficient conditions on an additive perturbation of an operator of the class (mathcal A_{m,K,chi}) in order that the perturbed operator also belong to such a class. Abstract results are used in the study of initial-boundary value problems for a system of partial differential equations with several fractional Riemann–Liouville derivatives of different orders with respect to time and for an equation with a fractional Prabhakar derivative with respect to time.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131827954","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
Shadowing property for nonautonomous dynamical systems 非自治动力系统的阴影性质
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-50-61
Свойство Отслеживания, Для Неавтономных, Динамических Систем, М.Л. Бланк
{"title":"Shadowing property for nonautonomous dynamical systems","authors":"Свойство Отслеживания, Для Неавтономных, Динамических Систем, М.Л. Бланк","doi":"10.22363/2413-3639-2023-69-1-50-61","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-50-61","url":null,"abstract":"A new approach based on the analysis of the influence of a single perturbation is proposed as a test for the shadowing property for a broad class of dynamical systems (in particular, non-autonomous) under a variety of perturbations. Applications for several interesting cases are considered in detail.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"171 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117301333","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
Absence of positive solutions of some nonlinear inequalities with transformations of the argument in a half-space 半空间中若干非线性不等式的无正解及其变换
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2022-69-1-62-72
E. Galakhov, O. Salieva
{"title":"Absence of positive solutions of some nonlinear inequalities with transformations of the argument in a half-space","authors":"E. Galakhov, O. Salieva","doi":"10.22363/2413-3639-2022-69-1-62-72","DOIUrl":"https://doi.org/10.22363/2413-3639-2022-69-1-62-72","url":null,"abstract":"We prove the absence of positive solutions for some semilinear elliptic partial differential inequalities with transformations of the argument in a half-space. The proofs are based on the test functions method.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128762683","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
Smoothness of generalized solutions to the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions on the boundary of adjacent subdomains 邻子域边界上具有正交各向异性收缩的强椭圆型泛函微分方程Dirichlet问题广义解的光滑性
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-152-165
A. Tasevich
{"title":"Smoothness of generalized solutions to the Dirichlet problem for strongly elliptic functional differential equations with orthotropic contractions on the boundary of adjacent subdomains","authors":"A. Tasevich","doi":"10.22363/2413-3639-2023-69-1-152-165","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-152-165","url":null,"abstract":"The paper is devoted to the study of the smoothness of generalized solutions of the first boundaryvalue problem for a strongly elliptic functional differential equation containing orthotropic contraction transformations of the arguments of the unknown function in the leading part. The problem is considered in a circle, the coe cients of the equation are constant. Orthotropic contraction is understood as different contraction in different variables. Conditions for the conservation of smoothness on the boundaries of neighboring subdomains formed by the action of the contraction transformation group on a circle are found in explicit form for any right-hand side from the Lebesgue space.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121689394","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
Method of search functionals and its applications in fixed point and coincidence theory 搜索泛函的方法及其在不动点和符合理论中的应用
Contemporary Mathematics. Fundamental Directions Pub Date : 2023-03-31 DOI: 10.22363/2413-3639-2023-69-1-185-200
T. Fomenko
{"title":"Method of search functionals and its applications in fixed point and coincidence theory","authors":"T. Fomenko","doi":"10.22363/2413-3639-2023-69-1-185-200","DOIUrl":"https://doi.org/10.22363/2413-3639-2023-69-1-185-200","url":null,"abstract":"The paper contains a survey of several results from the author’s papers and joint papers by the author and Yu. N. Zakharyan, both on the zero existence and approximation for single-valued and multivalued (α, β)-search functionals, and also on the zero existence preservation for parametric family of such functionals, under the parameter changing. Some corollaries of these results in the fixed point and coincidence theory of single-valued and multi-valued mappings of metric spaces are also given. The comparison is provided with some known results by other authors. In the concluding part of the paper, we investigate the problem on the existence of a parameter-continuous single-valued branch of zeros for a parametric family of search functionals. A theorem on the existence of solution of this problem is proved.","PeriodicalId":280824,"journal":{"name":"Contemporary Mathematics. Fundamental Directions","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125400358","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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