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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
On absolute Cesáro summablity of Fourier series for almost-periodic functions with limiting points at zero 极限点为0的概周期函数的傅里叶级数的绝对Cesáro可和性
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-144
Y. Khasanov
{"title":"On absolute Cesáro summablity of Fourier series for almost-periodic functions with limiting points at zero","authors":"Y. Khasanov","doi":"10.13108/2016-8-4-144","DOIUrl":"https://doi.org/10.13108/2016-8-4-144","url":null,"abstract":"In the paper we establish some tests for absolute Cesáro summability of the Fourier series for almost periodic functions in the Besicovitch space. We consider the case, when the Fourier exponents have a limiting point at zero and as a structure characteristics of the studied function, we use a high order averaging modulus.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"69 2","pages":"144-151"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72417440","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
Minimal value for the type of an entire function of order $rhoin(0,,1)$, whose zeros lie in an angle and have a prescribed density $rhoin(0，，1)$阶的整个函数类型的最小值，其零点位于一个角度并且具有规定的密度
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-108
V. Sherstyukov
{"title":"Minimal value for the type of an entire function of order $rhoin(0,,1)$, whose zeros lie in an angle and have a prescribed density","authors":"V. Sherstyukov","doi":"10.13108/2016-8-1-108","DOIUrl":"https://doi.org/10.13108/2016-8-1-108","url":null,"abstract":". In the work we find the minimal value that can be taken by the type of an entire function of order 𝜌 ∈ (0 , 1) with zeroes of prescribed upper and lower densities and located in an angle of a fixed opening less than 𝜋 . The main theorem generalizes the previous result by the author (the zeroes lie on one ray) and by A.Yu. Popov (only the upper density of zeros was taken into consideration). We distinguish and study in detail the case when the an entire function has a measurable sequence of zeroes. We provide applications of the obtained results to the uniqueness theorems for entire functions and to the completeness of exponential systems in the space of analytic in a circle functions with the standard topology of uniform convergence on compact sets.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"52 1","pages":"108-120"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72543994","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
Periodic solutions of convolution type equations with monotone nonlinearity 具有单调非线性的卷积型方程的周期解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-1-20
S. Askhabov
{"title":"Periodic solutions of convolution type equations with monotone nonlinearity","authors":"S. Askhabov","doi":"10.13108/2016-8-1-20","DOIUrl":"https://doi.org/10.13108/2016-8-1-20","url":null,"abstract":"By the method of monotone operators we establish theorems on global existence and uniqueness, as well as estimats and methods of finding the solutions for various classes of nonlinear convolution type integral equations in the real space of 2πperiodic functions Lp(−π, π).","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"91 1","pages":"20-34"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73162029","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
On simultaneous solution of the KdV equation and a fifth-order differential equation KdV方程与五阶微分方程的联立解
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-52
R. Garifullin
{"title":"On simultaneous solution of the KdV equation and a fifth-order differential equation","authors":"R. Garifullin","doi":"10.13108/2016-8-4-52","DOIUrl":"https://doi.org/10.13108/2016-8-4-52","url":null,"abstract":"In the paper we consider an universal solution to the KdV equation. This solution also satisfies a fifth order ordinary differential equation. We pose the problem on studying the behavior of this solution as t → ∞. For large time, the asymptotic solution has different structure depending on the slow variable s = x2/t. We construct the asymptotic solution in the domains s < −3/4, −3/4 < s < 5/24 and in the vicinity of the point s = −3/4. It is shown that a slow modulation of solution’s parameters in the vicinity of the point s = −3/4 is described by a solution to Painlevé IV equation.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"104 1","pages":"52-61"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89935774","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: 4
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
Degenerate fractional differential equations in locally convex spaces with a $sigma$-regular pair of operators 用正则算子对退化局部凸空间中的分数阶微分方程
IF 0.5
Ufa Mathematical Journal Pub Date : 2016-01-01 DOI: 10.13108/2016-8-4-98
M. Kostic, V. Fedorov
{"title":"Degenerate fractional differential equations in locally convex spaces with a $sigma$-regular pair of operators","authors":"M. Kostic, V. Fedorov","doi":"10.13108/2016-8-4-98","DOIUrl":"https://doi.org/10.13108/2016-8-4-98","url":null,"abstract":"We consider a degenerate fractional order differential equationDα t Lu(t) = Mu(t) in a Hausdorff sequentially complete locally convex space. Under the p-regularity of the operator pair (L,M), we find the phase space of the equation and the family of its resolving operators. We show that the identity image of the latter coincides with the phase space. We prove an unique solvability theorem and obtain the form of the solution to the Cauchy problem for the corresponding inhomogeneous equation. We give an example of application the obtained abstract results to studying the solvability of the initial boundary value problems for the partial differential equations involving entire functions on an unbounded operator in a Banach space, which is a specially constructed Frechét space. It allows us to consider, for instance, a periodic in a spatial variable x problem for the equation with a shift along x and with a fractional order derivative with respect to time t.","PeriodicalId":43644,"journal":{"name":"Ufa Mathematical Journal","volume":"2007 1","pages":"98-110"},"PeriodicalIF":0.5,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89513257","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
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