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Bulletin of the Karaganda University-Mathematics最新文献

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On the behaviors of solutions of a nonlinear diffusion system with a source and nonlinear boundary conditions 论具有源和非线性边界条件的非线性扩散系统解的行为
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/28-45
M. Aripov, Z. Rakhmonov, A.A. Alimov
{"title":"On the behaviors of solutions of a nonlinear diffusion system with a source and nonlinear boundary conditions","authors":"M. Aripov, Z. Rakhmonov, A.A. Alimov","doi":"10.31489/2024m1/28-45","DOIUrl":"https://doi.org/10.31489/2024m1/28-45","url":null,"abstract":"We study the global solvability and unsolvability of a nonlinear diffusion system with nonlinear boundary conditions in the case of slow diffusion. We obtain the critical exponent of the Fujita type and the critical global existence exponent, which plays a significant part in analyzing the qualitative characteristics of nonlinear models of reaction-diffusion, heat transfer, filtration, and other physical, chemical, and biological processes. In the global solvability case, the key components of the asymptotic solutions are obtained. Iterative methods, which quickly converge to the exact solution while maintaining the qualitative characteristics of the nonlinear processes under study, are known to require the presence of an appropriate initial approximation. This presents a significant challenge for the numerical solution of nonlinear problems. A successful selection of initial approximations allows for the resolution of this challenge, which depends on the value of the numerical parameters of the equation, which are primarily in the computations recommended using an asymptotic formula. Using the asymptotics of self-similar solutions as the initial approximation for the iterative process, numerical calculations and analysis of the results are carried out. The outcomes of numerical experiments demonstrate that the results are in excellent accord with the physics of the process under consideration of the nonlinear diffusion system.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366908","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
On solvability of the inverse problem for a fourth-order parabolic equation with a complex-valued coefficient 论带复值系数的四阶抛物方程逆问题的可解性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/60-72
A. Imanbetova, A. Sarsenbi, B. Seilbekov
{"title":"On solvability of the inverse problem for a fourth-order parabolic equation with a complex-valued coefficient","authors":"A. Imanbetova, A. Sarsenbi, B. Seilbekov","doi":"10.31489/2024m1/60-72","DOIUrl":"https://doi.org/10.31489/2024m1/60-72","url":null,"abstract":"In this paper, the inverse problem for a fourth-order parabolic equation with a variable complex-valued coefficient is studied by the method of separation of variables. The properties of the eigenvalues of the Dirichlet and Neumann boundary value problems for a non-self-conjugate fourth-order ordinary differential equation with a complex-valued coefficient are established. Known results on the Riesz basis property of eigenfunctions of boundary value problems for ordinary differential equations with strongly regular boundary conditions in the space L2(−1,1) are used. On the basis of the Riesz basis property of eigenfunctions, formal solutions of the problems under study are constructed and theorems on the existence and uniqueness of solutions are proved. When proving theorems on the existence and uniqueness of solutions, the Bessel inequality for the Fourier coefficients of expansions of functions from space L2(−1,1) into a Fourier series in the Riesz basis is widely used. The representations of solutions in the form of Fourier series in terms of eigenfunctions of boundary value problems for a fourth-order equation with involution are derived. The convergence of the obtained solutions is discussed.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367001","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
Isomorphism Theorems of a Series Sum and the Improper Integral 数列和与不完全积分的同构定理
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/128-139
V. P. Malyshev, S. Kazhikenova, A. M. Makasheva, A.Sh. Kazhikenova
{"title":"Isomorphism Theorems of a Series Sum and the Improper Integral","authors":"V. P. Malyshev, S. Kazhikenova, A. M. Makasheva, A.Sh. Kazhikenova","doi":"10.31489/2024m1/128-139","DOIUrl":"https://doi.org/10.31489/2024m1/128-139","url":null,"abstract":"The discrete and continuous dependencies’ relationship question has been investigated. An algorithm for determining the final and total series sums through the equivalence ratio of the series common term an and the an-model function improper integral mean value within the change unit interval based on the extended integral Cauchy convergence criterion has been developed. Examples of determining for the statistical sum in the Boltzmann distribution, for the first time directly expressed through an-model function. This eliminates the need for calculations to accumulate the sum of the series up to a value that is specified by a certain accuracy of this sum. In addition, it allows in this case to vary the energy variation interval with any given accuracy. The conducted studies allow solving both theoretical and practical problems of physics and materials science, directly using the Boltzmann distribution (energy spectrum) to calculate the entropy, which determines the loss of thermal energy in technological processes.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140367842","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
Some properties of the one-dimensional potentials 一维势的一些特性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/101-111
T.Sh. Kalmenov, A. Kadirbek, A. Kydyrbaikyzy
{"title":"Some properties of the one-dimensional potentials","authors":"T.Sh. Kalmenov, A. Kadirbek, A. Kydyrbaikyzy","doi":"10.31489/2024m1/101-111","DOIUrl":"https://doi.org/10.31489/2024m1/101-111","url":null,"abstract":"The main aim of this paper is to study the properties of the one-dimensional potentials. In this paper, we have studied the connection between the one-dimensional potentials and the self-adjoint part of the operator LK−1, which LK−1 is the solution to the one-dimensional Cauchy problem. Moreover, a new method is used that allows us to reduce the spectral problem for the Helmholtz potential to the equivalent problem.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140365369","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
A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay 一类具有固定大延迟的奇异扰动差分方程的新型数值方案
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/194-207
E. Srinivas, K. Phaneendra
{"title":"A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay","authors":"E. Srinivas, K. Phaneendra","doi":"10.31489/2024m1/194-207","DOIUrl":"https://doi.org/10.31489/2024m1/194-207","url":null,"abstract":"A trigonometric spline based computational technique is suggested for the numerical solution of layer behavior differential-difference equations with a fixed large delay. The continuity of the first order derivative of the trigonometric spline at the interior mesh point is used to develop the system of difference equations. With the help of singular perturbation theory, a fitting parameter is inserted into the difference scheme to minimize the error in the solution. The method is examined for convergence. We have also discussed the impact of shift or delay on the boundary layer. The maximum absolute errors in comparison to other approaches in the literature are tallied, and layer behavior is displayed in graphs, to demonstrate the feasibility of the suggested numerical method.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140364964","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
Existence of Hilfer fractional neutral stochastic differential systems with infinite delay 具有无限延迟的 Hilfer 分数中性随机微分系统的存在性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/174-193
S. Sivasankar, R. Udhayakumar, V. Muthukumaran, G. Gokul, S. Al-Omari
{"title":"Existence of Hilfer fractional neutral stochastic differential systems with infinite delay","authors":"S. Sivasankar, R. Udhayakumar, V. Muthukumaran, G. Gokul, S. Al-Omari","doi":"10.31489/2024m1/174-193","DOIUrl":"https://doi.org/10.31489/2024m1/174-193","url":null,"abstract":"The goal of this study is to propose the existence of mild solutions to delay fractional neutral stochastic differential systems with almost sectorial operators involving the Hilfer fractional (HF) derivative in Hilbert space, which generalized the famous Riemann-Liouville fractional derivative. The main techniques rely on the basic principles and concepts from fractional calculus, semigroup theory, almost sectorial operators, stochastic analysis, and the Mönch fixed point theorem via the measure of noncompactness (MNC). Particularly, the existence result of the equation is obtained under some weakly compactness conditions. An example is given at the end of this article to show the applications of the obtained abstract results.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368046","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
Factorization of abstract operators into two second degree operators and its applications to integro-differential equations 将抽象算子分解为两个二阶算子及其在积分微分方程中的应用
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/149-161
I. Parasidis, E. Providas
{"title":"Factorization of abstract operators into two second degree operators and its applications to integro-differential equations","authors":"I. Parasidis, E. Providas","doi":"10.31489/2024m1/149-161","DOIUrl":"https://doi.org/10.31489/2024m1/149-161","url":null,"abstract":"Boundary value problem B1x = f with an abstract linear operator B1, corresponding to an Fredholm integro-differential equation with ordinary or partial differential operator is researched. An exact solution to B1x = f in the case when a bijective operator B1 has a factorization of the form B1 =BB0 where B and B0 are two linear more simple than B1 second degree abstract operators, received. Conditions for factorization of the operator B1 and a criterion for bijectivity of B1 are found.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140365462","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
Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space 多权重各向异性索波列夫类型空间的嵌入
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/73-83
G. Iskakova, M. S. Aitenova, A. K. Sexenbayeva
{"title":"Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space","authors":"G. Iskakova, M. S. Aitenova, A. K. Sexenbayeva","doi":"10.31489/2024m1/73-83","DOIUrl":"https://doi.org/10.31489/2024m1/73-83","url":null,"abstract":"Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368449","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
Problem for differential-algebraic equations with a significant loads 有重要负载的微分代数方程问题
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/46-59
A. Assanova, Zh. M. Kadirbayeva, R. A. Medetbekova, S. Mynbayeva
{"title":"Problem for differential-algebraic equations with a significant loads","authors":"A. Assanova, Zh. M. Kadirbayeva, R. A. Medetbekova, S. Mynbayeva","doi":"10.31489/2024m1/46-59","DOIUrl":"https://doi.org/10.31489/2024m1/46-59","url":null,"abstract":"In this article, the problem for a differential-algebraic equation with a significant loads is studied. Unlike previously studied problems for differential equations with a significant loads, in the considered equation, there is a matrix in the left part with a derivative that is not invertible. Therefore, the system of equations includes both differential and algebraic equations. To solve the problem, we propose a modification of the Dzhumabaev’s parametrization method. The considered problem is reduced to a parametric problem for the differential-algebraic equation with significant loads. We apply the Weierstrass canonical form to this problem. We obtain parametric initial value problem for a differential equations and an algebraic equations with a significant loads. The solvability conditions for the considered problem are established.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366090","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
The cosemanticness of Kaiser hulls of fixed classes of models 固定类别模型的凯泽壳的共语性
IF 0.6
Bulletin of the Karaganda University-Mathematics Pub Date : 2024-03-29 DOI: 10.31489/2024m1/208-217
A. Yeshkeyev, I. Tungushbayeva, A. K. Koshekova
{"title":"The cosemanticness of Kaiser hulls of fixed classes of models","authors":"A. Yeshkeyev, I. Tungushbayeva, A. K. Koshekova","doi":"10.31489/2024m1/208-217","DOIUrl":"https://doi.org/10.31489/2024m1/208-217","url":null,"abstract":"In this article, within the framework of the study of Jonsson theories, the model-theoretic properties of cosemanticness classes belonging to the factor set of the Jonsson spectrum of an existentially closed models’ subclass of some Jonsson theory in a fixed language were studied. Various results have been obtained. In particular, the properties of the cosemanticness of models and classes of models are considered; some results concerning the Jonsson equivalence in generalization for classes of existentially closed models are obtained; a criterion for the cosemanticness of J-classes in connection with their Kaiser hulls has been found.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140366270","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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