In the paper, we consider simultaneous approximation of a pair of analytic functions by discrete shifts $zeta_{u_N}(s+ikh_1; ga)$ and $zeta_{u_N}(s+ikh_2, alpha; gb)$ of the absolutely convergent Dirichlet series connected to the periodic zeta-function with multiplicative sequence $ga$, and the periodic Hurwitz zeta-function, respectively. We suppose that $u_Ntoinfty$ and $u_Nll N^2$ as $Ntoinfty$, and the set ${(h_1log p:! pin! PP), (h_2log(m+alpha): min NN_0), 2pi}$ is linearly independent over $QQ$.
{"title":"A DISCRETE VERSION OF THE MISHOU THEOREM RELATED TO PERIODIC ZETA-FUNCTIONS","authors":"A. Balčiūnas, M. Jasas, Audronė Rimkevičienė","doi":"10.3846/mma.2024.19502","DOIUrl":"https://doi.org/10.3846/mma.2024.19502","url":null,"abstract":"In the paper, we consider simultaneous approximation of a pair of analytic functions by discrete shifts $zeta_{u_N}(s+ikh_1; ga)$ and $zeta_{u_N}(s+ikh_2, alpha; gb)$ of the absolutely convergent Dirichlet series connected to the periodic zeta-function with multiplicative sequence $ga$, and the periodic Hurwitz zeta-function, respectively. We suppose that $u_Ntoinfty$ and $u_Nll N^2$ as $Ntoinfty$, and the set ${(h_1log p:! pin! PP), (h_2log(m+alpha): min NN_0), 2pi}$ is linearly independent over $QQ$.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, our focus lies in addressing the Dirichlet problem associated with a specific class of critical anisotropic elliptic equations of Schrödinger-Kirchhoff type. These equations incorporate variable exponents and a real positive parameter. Our objective is to establish the existence of at least one solution to this problem.
{"title":"THE DIRICHLET PROBLEM FOR A CLASS OF ANISOTROPIC SCHRÖDINGER-KIRCHHOFF-TYPE EQUATIONS WITH CRITICAL EXPONENT","authors":"N. C. Eddine, Anh Tuan Nguyen, M. Ragusa","doi":"10.3846/mma.2024.19006","DOIUrl":"https://doi.org/10.3846/mma.2024.19006","url":null,"abstract":"In this paper, our focus lies in addressing the Dirichlet problem associated with a specific class of critical anisotropic elliptic equations of Schrödinger-Kirchhoff type. These equations incorporate variable exponents and a real positive parameter. Our objective is to establish the existence of at least one solution to this problem.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we focus on the well-posedness problem of the three-dimensional incompressible viscous and resistive Hall-magnetohydrodynamics system (Hall-MHD) with variable density. We mainly prove the existence and uniqueness issues of the density-dependent incompressible Hall-magnetohydrodynamic system in critical spaces on R3.
{"title":"THE GLOBAL STRONG SOLUTIONS OF THE 3D INCOMPRESSIBLE HALL-MHD SYSTEM WITH VARIABLE DENSITY","authors":"Shu An, Jing-Yao Chen, Bin Han","doi":"10.3846/mma.2024.17776","DOIUrl":"https://doi.org/10.3846/mma.2024.17776","url":null,"abstract":"In this paper, we focus on the well-posedness problem of the three-dimensional incompressible viscous and resistive Hall-magnetohydrodynamics system (Hall-MHD) with variable density. We mainly prove the existence and uniqueness issues of the density-dependent incompressible Hall-magnetohydrodynamic system in critical spaces on R3.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.
{"title":"SOME CONSIDERATIONS ON NUMERICAL METHODS FOR CAUCHY SINGULAR INTEGRAL EQUATIONS ON THE REAL LINE","authors":"M. R. Capobianco, G. Criscuolo","doi":"10.3846/mma.2024.18688","DOIUrl":"https://doi.org/10.3846/mma.2024.18688","url":null,"abstract":"Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140379903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Lerch zeta-function $L(lambda, alpha,s)$, $s=sigma+it$, depends on two real parameters $lambda$ and $01$, is defined by the Dirichlet series $sum_{m=0}^infty ee^{2pi ilambda m} (m+alpha)^{-s}$, and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts $(L(lambda_1, alpha_1, s+ikh_1), dots, L(lambda_r, alpha_r, s+ikh_r))$, $k=0, 1, dots$, with arbitrary $lambda_j$, $00$, $j=1, dots, r$. We prove that there exists a non-empty closed set of analytic functions on the critical strip $1/2
{"title":"JOINT DISCRETE APPROXIMATION OF ANALYTIC FUNCTIONS BY SHIFTS OF LERCH ZETA-FUNCTIONS","authors":"A. Laurinčikas, Toma Mikalauskaitė, D. Šiaučiūnas","doi":"10.3846/mma.2024.19493","DOIUrl":"https://doi.org/10.3846/mma.2024.19493","url":null,"abstract":"The Lerch zeta-function $L(lambda, alpha,s)$, $s=sigma+it$, depends on two real parameters $lambda$ and $0<alphaleqslant 1$, and, for $sigma>1$, is defined by the Dirichlet series $sum_{m=0}^infty ee^{2pi ilambda m} (m+alpha)^{-s}$, and by analytic continuation elsewhere. In the paper, we consider the joint approximation of collections of analytic functions by discrete shifts $(L(lambda_1, alpha_1, s+ikh_1), dots, L(lambda_r, alpha_r, s+ikh_r))$, $k=0, 1, dots$, with arbitrary $lambda_j$, $0<alpha_jleqslant 1$ and $h_j>0$, $j=1, dots, r$. We prove that there exists a non-empty closed set of analytic functions on the critical strip $1/2<sigma<1$ which is approximated by the above shifts. It is proved that the set of shifts approximating a given collection of analytic functions has a positive lower density. The case of positive density also is discussed. A generalization for some compositions is given.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The article investigates a discrete Sturm–Liouville problem with one natural boundary condition and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures.
{"title":"INVESTIGATION OF A DISCRETE STURM–LIOUVILLE PROBLEM WITH TWO-POINT NONLOCAL BOUNDARY CONDITION AND NATURAL APPROXIMATION OF A DERIVATIVE IN BOUNDARY CONDITION","authors":"Kristina Bingelė, A. Štikonas","doi":"10.3846/mma.2024.19829","DOIUrl":"https://doi.org/10.3846/mma.2024.19829","url":null,"abstract":"The article investigates a discrete Sturm–Liouville problem with one natural boundary condition and another nonlocal two-point boundary condition. We analyze zeroes, poles and critical points of the characteristic function and how the properties of this function depend on parameters in nonlocal boundary condition. Properties of the Spectrum Curves are formulated and illustrated in figures.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.
{"title":"SIMULTANEOUS INVERSION OF THE SOURCE TERM AND INITIAL VALUE OF THE TIME FRACTIONAL DIFFUSION EQUATION","authors":"Fan Yang, Jian-ming Xu, Xiao-Xiao Li","doi":"10.3846/mma.2024.18133","DOIUrl":"https://doi.org/10.3846/mma.2024.18133","url":null,"abstract":"In this paper, the problem we investigate is to simultaneously identify the source term and initial value of the time fractional diffusion equation. This problem is ill-posed, i.e., the solution (if exists) does not depend on the measurable data. We give the conditional stability result under the a-priori bound assumption for the exact solution. The modified Tikhonov regularization method is used to solve this problem, and under the a-priori and the a-posteriori selection rule for the regularization parameter, the convergence error estimations for this method are obtained. Finally, numerical example is given to prove the effectiveness of this regularization method.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140378939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza
In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.
{"title":"A MODIFIED NEWTON-SECANT METHOD FOR SOLVING NONSMOOTH GENERALIZED EQUATIONS","authors":"Vitaliano de Sousa Amaral, Paulo Sérgio Marques dos Santos, Gilson N. Silva, Sissy Souza","doi":"10.3846/mma.2024.18680","DOIUrl":"https://doi.org/10.3846/mma.2024.18680","url":null,"abstract":"In this paper, we study the solvability of nonsmooth generalized equations in Banach spaces using a modified Newton-secant method, by assuming a Hölder condition. Also, we generalize a Dennis-Moré theorem to characterize the superlinear convergence of the proposed method applied to nonsmooth generalized equations under strong metric subregularity. Numerical examples are provided to illustrate the effectiveness of our approach.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380316","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we consider the equation $-textrm{div},(a(x,u,Du){=}H(x,u,Du){+}frac{a_{0}(x)}{vert u vert^{theta}}+chi_{{uneq 0}},f(x)$ {in} $Omega$, with boundary conditions $u=0$ {on} $partialOmega$, where $Omega$ is an open bounded subset of $mathbb{R}^{N}$, $1 0$, $0
在本文中，我们考虑方程 $-textrm{div},(a(x,u,Du){=}H(x,u,Du){+}frac{a_{0}(x)}{vert uvert^{theta}}+chi_{uneq 0}}、f(x)$ {in} $Omega$, with boundary conditions$u=0$ {on} $partialOmega$, where $Omega$ is an open bounded subset of $mathbb{R}^{N}$、$1 0$, $0
{"title":"A SINGULAR NONLINEAR PROBLEMS WITH NATURAL GROWTH IN THE GRADIENT","authors":"B. Hamour","doi":"10.3846/mma.2024.17948","DOIUrl":"https://doi.org/10.3846/mma.2024.17948","url":null,"abstract":"In this paper, we consider the equation \u0000$-textrm{div},(a(x,u,Du){=}H(x,u,Du){+}frac{a_{0}(x)}{vert u vert^{theta}}+chi_{{uneq 0}},f(x)$\u0000 {in} $Omega$, with boundary conditions\u0000$u=0$ {on} $partialOmega$, \u0000where $Omega$ is an open bounded subset of $mathbb{R}^{N}$, $1<p< N$, $-mbox{div}(a(x,u,Du))$ is a Leray-Lions operator defined on $W_{0}^{1,p}(Omega)$, $a_{0}in L^{N/p}(Omega )$, $a_{0}> 0$, $0<thetaleq 1$, $chi_{{uneq 0}}$ is a characteristic function, $fin L^{N/p}(Omega)$\u0000and $H(x,s,xi)$ is a Carath'eodory function such that $-c_{0}, a(x,s,xi)xi,leq H(x,s,xi),mbox {sign}(s)leq gamma,a(x,s,xi)xi quad\u0000 mbox {a.e. } xin Omega , forall sinmathbb{R},, ,\u0000 forallxi in mathbb{R}^{N}.\u0000 $\u0000For $Vert a_{0}Vert_{N/p}$ and $Vert fVert_{N/p}$ sufficiently small, we prove the existence of at least one solution $u$ of this problem which is moreover such that the function $exp(delta vert u vert)-1 $ belongs to $W_{0}^{1,p}(Omega)$ for some $deltageq gamma$. This solution satisfies some a priori estimates in $W_0^{1,p}(Omega)$.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140380476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Erick Delgado Moya, Alain Pietrus, Séverine Bernard
In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.
{"title":"MATHEMATICAL MODEL FOR THE STUDY OF OBESITY IN A POPULATION AND ITS IMPACT ON THE GROWTH OF DIABETES","authors":"Erick Delgado Moya, Alain Pietrus, Séverine Bernard","doi":"10.3846/mma.2023.17510","DOIUrl":"https://doi.org/10.3846/mma.2023.17510","url":null,"abstract":"In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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