In the present paper we consider gradient type iterative methods for solving the Stokes problem in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of grids for solving two-dimensional problem with a known analytic solution.
{"title":"Gradient methods for solving Stokes problem","authors":"I. I. Golichev, Timur Sharipov, N. I. Luchnikova","doi":"10.13108/2016-8-2-22","DOIUrl":"https://doi.org/10.13108/2016-8-2-22","url":null,"abstract":"In the present paper we consider gradient type iterative methods for solving the Stokes problem in bounded regions, where the pressure serves as the control; they are obtained by reducing the problem to that of a variational type. In the differential form the proposed methods are very close to the algorithms in the Uzawa family. We construct consistent finite-difference algorithms and we present their approbation on the sequence of grids for solving two-dimensional problem with a known analytic solution.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"22-38"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88722139","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}
. In this paper we consider exponential series with complex exponents, whose real and imaginary parts are integer. We prove that each function analytical in the vicinity of the closure of a bounded convex domain in the complex plain can be expanded into the above mentioned series and this series converges absolutely inside this domain and uniformly on compact subsets. The result is based on constructing a regular subset with a prescribed angular density of the sequence of all complex numbers, whose real and imaginary parts are integer.
{"title":"Representation of analytic functions","authors":"A. I. Abdulnagimov, A. Krivosheev","doi":"10.13108/2016-8-4-3","DOIUrl":"https://doi.org/10.13108/2016-8-4-3","url":null,"abstract":". In this paper we consider exponential series with complex exponents, whose real and imaginary parts are integer. We prove that each function analytical in the vicinity of the closure of a bounded convex domain in the complex plain can be expanded into the above mentioned series and this series converges absolutely inside this domain and uniformly on compact subsets. The result is based on constructing a regular subset with a prescribed angular density of the sequence of all complex numbers, whose real and imaginary parts are integer.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"52 1","pages":"3-23"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78928491","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}
{"title":"On solutions of second order elliptic equations in cylindrical domains","authors":"A. V. Neklyudov","doi":"10.13108/2016-8-4-131","DOIUrl":"https://doi.org/10.13108/2016-8-4-131","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"19 1","pages":"131-143"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79290141","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}
. We consider a hydrodynamic type system, waterbag model, that admits a dispersionless Lax representation with a logarithmic Lax function. Using the Lax representation, we construct a recursion operator of the system. We note that the constructed recursion operator is not compatible with the natural Hamiltonian representation of the system.
{"title":"Recursion operator for a system with non-rational Lax representation","authors":"K. Zheltukhin","doi":"10.13108/2016-8-2-112","DOIUrl":"https://doi.org/10.13108/2016-8-2-112","url":null,"abstract":". We consider a hydrodynamic type system, waterbag model, that admits a dispersionless Lax representation with a logarithmic Lax function. Using the Lax representation, we construct a recursion operator of the system. We note that the constructed recursion operator is not compatible with the natural Hamiltonian representation of the system.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"175 1","pages":"112-118"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78463150","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}
In the work we study the properties of the resolvent of the Laplace-Beltrami operator on a two-dimensional sphere S2. We obtain the regularized trace formula for the Laplace-Beltrami operator perturbed by the operator of multiplication by a function in W 1 2 (S 2).
{"title":"Properties of the resolvent of the Laplace operator on a two-dimensional sphere and a trace formula","authors":"A. Atnagulov, V. Sadovnichii, Z. Fazullin","doi":"10.13108/2016-8-3-22","DOIUrl":"https://doi.org/10.13108/2016-8-3-22","url":null,"abstract":"In the work we study the properties of the resolvent of the Laplace-Beltrami operator on a two-dimensional sphere S2. We obtain the regularized trace formula for the Laplace-Beltrami operator perturbed by the operator of multiplication by a function in W 1 2 (S 2).","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"27 1","pages":"22-40"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73507464","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}
We show that the existence of unconditional exponential bases is not determined by the growth characteristics of a weight function. In order to do this, we construct examples of convex weights with arbitrarily slow growth near the boundary such that unconditional exponential bases do not exist in the corresponding space.
{"title":"On unconditional exponential bases in weak weighted spaces on segment","authors":"K. P. Isaev, A. Lutsenko, R. S. Yulmukhametov","doi":"10.13108/2016-8-4-88","DOIUrl":"https://doi.org/10.13108/2016-8-4-88","url":null,"abstract":"We show that the existence of unconditional exponential bases is not determined by the growth characteristics of a weight function. In order to do this, we construct examples of convex weights with arbitrarily slow growth near the boundary such that unconditional exponential bases do not exist in the corresponding space.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"14 1","pages":"88-97"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84267877","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}
{"title":"The problem of Steklov type in a half-cylinder with a small cavity","authors":"D. B. Davletov, D. V. Kozhevnikov","doi":"10.13108/2016-8-4-62","DOIUrl":"https://doi.org/10.13108/2016-8-4-62","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"30 1 1","pages":"62-87"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85528555","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}
. In this paper we study the solvability of one boundary value problem for an inhomogeneous polyharmonic equation. As a boundary operator, we consider a differen-tiation operator of fractional order in the Hadamard sense. The considered problem is a generalization of the known Neumann problem.
{"title":"On solvability of a boundary value problem for an inhomogeneous polyharmonic equation with a fractional order boundary operator","authors":"B. Turmetov","doi":"10.13108/2016-8-3-155","DOIUrl":"https://doi.org/10.13108/2016-8-3-155","url":null,"abstract":". In this paper we study the solvability of one boundary value problem for an inhomogeneous polyharmonic equation. As a boundary operator, we consider a differen-tiation operator of fractional order in the Hadamard sense. The considered problem is a generalization of the known Neumann problem.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"8 1","pages":"155-170"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82029911","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}
We consider an elliptic operator in a multi-dimensional domain with frequent alternation of Dirichlet and Robin conditions. We study the case, when the homogenized operator has Robin condition with an additional coefficient generated by the geometry of the alternation. We prove the norm resolvent convergence of the perturbed operator to the homogenized one and obtain the estimate for the convergence rate. We construct the complete asymptotic expansion for the resolvent in the case, when it acts on sufficiently smooth functions.
{"title":"On resolvent of multi-dimensional operators with frequent alternation of boundary conditions: Critical case","authors":"T. F. Sharapov","doi":"10.13108/2016-8-2-65","DOIUrl":"https://doi.org/10.13108/2016-8-2-65","url":null,"abstract":"We consider an elliptic operator in a multi-dimensional domain with frequent alternation of Dirichlet and Robin conditions. We study the case, when the homogenized operator has Robin condition with an additional coefficient generated by the geometry of the alternation. We prove the norm resolvent convergence of the perturbed operator to the homogenized one and obtain the estimate for the convergence rate. We construct the complete asymptotic expansion for the resolvent in the case, when it acts on sufficiently smooth functions.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"7 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75161094","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：