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Numerical modeling of the non-equilibrium sorption process 非平衡吸附过程的数值模拟
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-39
I. A. Kaliev, S. Mukhambetzhanov, G. S. Sabitova
{"title":"Numerical modeling of the non-equilibrium sorption process","authors":"I. A. Kaliev, S. Mukhambetzhanov, G. S. Sabitova","doi":"10.13108/2016-8-2-39","DOIUrl":"https://doi.org/10.13108/2016-8-2-39","url":null,"abstract":". Filtration in porous media of fluids and gases containing associated with them (dissolved, particulate) solid substances is accompanied by the diffusion of these substances and mass transfer between the liquid (gas) and solid stages. The most common types of mass transfer are sorption and desorption, ion exchange, dissolution and crystallization, mudding, sulfation and suffusion, waxing. We consider the system of equations modeling the process of non-equilibrium sorption. We formulate a difference approximation of the differential problem by an implicit scheme. The solution to the difference problem is constructed by the sweep method. Basing on the numerical results, we can conclude the following: as the relaxation time decreases, the solution to the non-equilibrium problem tends to the solution of the equilibrium problem as the time increases.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"7 1","pages":"39-43"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75522598","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
Asymptotic expansions of solutions to Dirichlet problem for elliptic equation with singularities 带奇点椭圆型方程Dirichlet问题解的渐近展开式
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-97
D. Tursunov, U. Erkebaev
{"title":"Asymptotic expansions of solutions to Dirichlet problem for elliptic equation with singularities","authors":"D. Tursunov, U. Erkebaev","doi":"10.13108/2016-8-1-97","DOIUrl":"https://doi.org/10.13108/2016-8-1-97","url":null,"abstract":"The paper proposes an analogue of Vishik-Lyusternik-Vasileva-Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to bisingular perturbed problems. By means of this method we construct the uniform asymptotic expansion for the solution to the Dirichlet problem for bisingular perturbed second order elliptic equation with two independent variables in a circle. By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"48 1","pages":"97-107"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88009837","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: 11
On solutions of Cauchy problem for equation $u_{xx}+Q(x)u-P(u)=0$ without singularities in a given interval 方程$u_{xx}+Q(x)u- p (u)=0$在给定区间内无奇点的Cauchy问题的解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-24
G. Alfimov, P. P. Kizin
{"title":"On solutions of Cauchy problem for equation $u_{xx}+Q(x)u-P(u)=0$ without singularities in a given interval","authors":"G. Alfimov, P. P. Kizin","doi":"10.13108/2016-8-4-24","DOIUrl":"https://doi.org/10.13108/2016-8-4-24","url":null,"abstract":"The paper is devoted to Cauchy problem for equation uxx Qpxqu P puq 0, where Qpxq is a π-periodic function. It is known that for a wide class of the nonlinearities P puq the “most part” of solutions of Cauchy problem for this equation are singular, i.e., they tend to infinity at some finite point of the real axis. Earlier in the case P puq u3 this fact allowed us to propose an approach for a complete description of solutions to this equation bounded on R. One of the ingredients in this approach is the studying of the set U L introduced as the set of the points pu , u1 q in the initial data plane, for which the solutions to the Cauchy problem up0q u , uxp0q u 1 are not singular in the segment r0;Ls. In the present work we prove a series of statements on the set U L and on their base, we classify all possible type of the geometry of such sets. The presented results of the numerical calculations are in a good agreement with theoretical statements.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"157 1","pages":"24-41"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74191017","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
Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term 带源项的非线性分数扩散方程的对称约简与不变解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-111
Stanislav Yur'evich Lukashchuk
{"title":"Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term","authors":"Stanislav Yur'evich Lukashchuk","doi":"10.13108/2016-8-4-111","DOIUrl":"https://doi.org/10.13108/2016-8-4-111","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"88 18 1","pages":"111-122"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84068522","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: 12
Recursion operator for a system with non-rational Lax representation 具有非理性Lax表示的系统的递归算子
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-112
K. Zheltukhin
{"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}
引用次数: 0
Gradient methods for solving Stokes problem 求解Stokes问题的梯度方法
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-2-22
I. I. Golichev, Timur Sharipov, N. I. Luchnikova
{"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}
引用次数: 0
Asymptotics for the eigenvalues of a fourth order differential operator in a “degenerate” case 退化情况下四阶微分算子特征值的渐近性
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-3-79
Kh. K. Ishkin, Khairulla Khabibullovich Murtazin
{"title":"Asymptotics for the eigenvalues of a fourth order differential operator in a “degenerate” case","authors":"Kh. K. Ishkin, Khairulla Khabibullovich Murtazin","doi":"10.13108/2016-8-3-79","DOIUrl":"https://doi.org/10.13108/2016-8-3-79","url":null,"abstract":"In the paper we consider the operator L in L2[0,+∞) generated by the differential expression L(y) = y(4) − 2(p(x)y′)′ + q(x)y and boundary conditions y(0) = y′′(0) = 0 in the “degenerate” case, when the roots of associated characteristic equation has different growth rate at the infinity. Assuming a power growth for functions p and q, under some additional conditions of smoothness and regularity kind, we obtain an asymptotic equation for the spectrum allowing us to write out several first terms in the asymptotic expansion for the eigenvalues of the operator L.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"7 1","pages":"79-94"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82511363","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
Representation of analytic functions 解析函数的表示
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-3
A. I. Abdulnagimov, A. Krivosheev
{"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}
引用次数: 1
Modulo-loxodromic meromorphic functions in $mathbb Csetminus{0}$ $mathbb Csetminus{0}$中的模异亚纯函数
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-152
Andriy Yaroslavovych Khrystiyanyn, A. Kondratyuk
{"title":"Modulo-loxodromic meromorphic functions in $mathbb Csetminus{0}$","authors":"Andriy Yaroslavovych Khrystiyanyn, A. Kondratyuk","doi":"10.13108/2016-8-4-152","DOIUrl":"https://doi.org/10.13108/2016-8-4-152","url":null,"abstract":"","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"1 1","pages":"152-158"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78970022","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
On solutions of second order elliptic equations in cylindrical domains 柱面上二阶椭圆方程的解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-131
A. V. Neklyudov
{"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}
引用次数: 0
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