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International Journal of Differential Equations最新文献

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The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type 含摩擦型条件的混合边界条件的非稳态Boussinesq系统
IF 1.6
International Journal of Differential Equations Pub Date : 2020-09-03 DOI: 10.1155/2020/6096531
Tujin Kim
{"title":"The Nonsteady Boussinesq System with Mixed Boundary Conditions including Conditions of Friction Type","authors":"Tujin Kim","doi":"10.1155/2020/6096531","DOIUrl":"https://doi.org/10.1155/2020/6096531","url":null,"abstract":"In this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity, and shape of the boundary surface, we get variational formulation. The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. For the case of boundary conditions including the static pressure and stress, we prove that if the data of the problem are small enough and compatibility conditions at the initial instance are satisfied, then there exists a unique solution on the given interval. For the case of boundary conditions including the total pressure and total stress, we prove the existence of a solution without restriction on the data and parameters of the problem.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-25"},"PeriodicalIF":1.6,"publicationDate":"2020-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/6096531","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44353403","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: 3
Transmission Dynamics of Fractional Order Brucellosis Model Using Caputo–Fabrizio Operator 利用Caputo-Fabrizio算子的分数阶布鲁氏菌病模型的传播动力学
IF 1.6
International Journal of Differential Equations Pub Date : 2020-08-14 DOI: 10.1155/2020/2791380
Olumuyiwa James Peter
{"title":"Transmission Dynamics of Fractional Order Brucellosis Model Using Caputo–Fabrizio Operator","authors":"Olumuyiwa James Peter","doi":"10.1155/2020/2791380","DOIUrl":"https://doi.org/10.1155/2020/2791380","url":null,"abstract":"In this paper, a noninteger order Brucellosis model is developed by employing the Caputo–Fabrizio noninteger order operator. The approach of noninteger order calculus is quite new for such a biological phenomenon. We establish the existence, uniqueness, and stability conditions for the model via the fixed-point theory. The initial approachable approximate solutions are derived for the proposed model by applying the iterative Laplace transform technique. Finally, numerical simulations are conducted for the analytical results to visualize the effect of various parameters that govern the dynamics of infection, and the results are presented using plots.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/2791380","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46766433","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: 21
Stability of Fuzzy Dynamical Systems via Lyapunov Functions 基于Lyapunov函数的模糊动力系统稳定性
IF 1.6
International Journal of Differential Equations Pub Date : 2020-08-01 DOI: 10.1155/2020/6218424
A. El Allaoui, S. Melliani, L. S. Chadli
{"title":"Stability of Fuzzy Dynamical Systems via Lyapunov Functions","authors":"A. El Allaoui, S. Melliani, L. S. Chadli","doi":"10.1155/2020/6218424","DOIUrl":"https://doi.org/10.1155/2020/6218424","url":null,"abstract":"The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stability. Some examples are given to illustrate the obtained results.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/6218424","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45054133","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 One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces 关于S空间中一个具有分数微分算子的抛物型演化方程
IF 1.6
International Journal of Differential Equations Pub Date : 2020-07-18 DOI: 10.1155/2020/1673741
V. Gorodetskiy, R. Kolisnyk, N. Shevchuk
{"title":"On One Evolution Equation of Parabolic Type with Fractional Differentiation Operator in S Spaces","authors":"V. Gorodetskiy, R. Kolisnyk, N. Shevchuk","doi":"10.1155/2020/1673741","DOIUrl":"https://doi.org/10.1155/2020/1673741","url":null,"abstract":"In the paper, we investigate a nonlocal multipoint by a time problem for the evolution equation with the operator A � (I − Δ)ω/2, Δ � (d2/dx2), and ω ∈ [1; − 2) is a fixed parameter. )e operator A is treated as a pseudodifferential operator in a certain space of type S. )e solvability of this problem is proved. )e representation of the solution is given in the form of a convolution of the fundamental solution with the initial function which is an element of the space of generalized functions of ultradistribution type. )e properties of the fundamental solution are investigated. )e behavior of the solution at t⟶ +∞ (solution stabilization) in the spaces of generalized functions of type S′ and the uniform stabilization of the solution to zero on R are studied.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2020-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/1673741","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48383558","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
Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D 微可压缩流体的Bénard问题：三维存在性和非线性稳定性
IF 1.6
International Journal of Differential Equations Pub Date : 2020-07-08 DOI: 10.1155/2020/9610689
A. Passerini
{"title":"Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D","authors":"A. Passerini","doi":"10.1155/2020/9610689","DOIUrl":"https://doi.org/10.1155/2020/9610689","url":null,"abstract":"This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Benard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-11"},"PeriodicalIF":1.6,"publicationDate":"2020-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/9610689","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47832860","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
Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model 求解SEIR流行病模型的变分迭代法和微分变换法
IF 1.6
International Journal of Differential Equations Pub Date : 2020-07-02 DOI: 10.1155/2020/3521936
A. Harir, S. Melliani, H. E. Harfi, L. S. Chadli
{"title":"Variational Iteration Method and Differential Transformation Method for Solving the SEIR Epidemic Model","authors":"A. Harir, S. Melliani, H. E. Harfi, L. S. Chadli","doi":"10.1155/2020/3521936","DOIUrl":"https://doi.org/10.1155/2020/3521936","url":null,"abstract":"The aim of the present study is to analyze and find a solution for the model of nonlinear ordinary differential equations (ODEs) describing the so-called coronavirus (COVID-19), a deadly and most parlous virus The mathematical model based on four nonlinear ODEs is presented, and the corresponding numerical results are studied by applying the variational iteration method (VIM) and differential transformation method (DTM) [ABSTRACT FROM AUTHOR] Copyright of International Journal of Differential Equations is the property of Hindawi Limited and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission However, users may print, download, or email articles for individual use This abstract may be abridged No warranty is given about the accuracy of the copy Users should refer to the original published version of the material for the full abstract (Copyright applies to all Abstracts )","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-7"},"PeriodicalIF":1.6,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/3521936","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45577409","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: 26
Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation 可压缩双流体Euler-Maxwell方程解的整体存在性和渐近性
IF 1.6
International Journal of Differential Equations Pub Date : 2020-06-29 DOI: 10.1155/2020/4363296
Ismahan Binshati, H. Hattori
{"title":"Global Existence and Asymptotic Behavior of Solutions for Compressible Two-Fluid Euler–Maxwell Equation","authors":"Ismahan Binshati, H. Hattori","doi":"10.1155/2020/4363296","DOIUrl":"https://doi.org/10.1155/2020/4363296","url":null,"abstract":"We study the global existence and asymptotic behavior of the solutions for two-fluid compressible isentropic Euler–Maxwell equations by the Fourier transform and energy method. We discuss the case when the pressure for two fluids is not identical, and we also add friction between the two fluids. In addition, we discuss the rates of decay of norms for a linear system. Moreover, we use the result for estimates to prove the decay rates for the nonlinear systems.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-27"},"PeriodicalIF":1.6,"publicationDate":"2020-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4363296","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42569886","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
Stability Analysis of a Fractional-Order Model for Abstinence Behavior of Registration on the Electoral Lists 选举名单节制登记行为分数阶模型的稳定性分析
IF 1.6
International Journal of Differential Equations Pub Date : 2020-06-22 DOI: 10.1155/2020/4325640
O. Balatif, L. Boujallal, A. Labzai, Mostafa Rachik
{"title":"Stability Analysis of a Fractional-Order Model for Abstinence Behavior of Registration on the Electoral Lists","authors":"O. Balatif, L. Boujallal, A. Labzai, Mostafa Rachik","doi":"10.1155/2020/4325640","DOIUrl":"https://doi.org/10.1155/2020/4325640","url":null,"abstract":"In this work, we propose a fractional-order model that describes the dynamics of citizens who have the right to register on the electoral lists and the negative influence of abstainers on the potential electors. By using Routh–Hurwitz criteria and constructing Lyapunov functions, the local and the global stability of abstaining-free equilibrium and abstaining equilibrium are obtained. Finally, some numerical simulations are performed to verify the theoretical analysis, and they are given for different parameter setting of the order of derivative α.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/4325640","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42719531","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
Z-Control on COVID-19-Exposed Patients in Quarantine 新型冠状病毒暴露患者隔离z控
IF 1.6
International Journal of Differential Equations Pub Date : 2020-06-19 DOI: 10.1155/2020/7876146
Nita H. Shah, Nisha Sheoran, E. Jayswal
{"title":"Z-Control on COVID-19-Exposed Patients in Quarantine","authors":"Nita H. Shah, Nisha Sheoran, E. Jayswal","doi":"10.1155/2020/7876146","DOIUrl":"https://doi.org/10.1155/2020/7876146","url":null,"abstract":"In this paper, a mathematical model for diabetic or hypertensive patients exposed to COVID-19 is formulated along with a set of first-order nonlinear differential equations. The system is said to exhibit two equilibria, namely, exposure-free and endemic points. The reproduction number is obtained for each equilibrium point. Local stability conditions are derived for both equilibria, and global stability is studied for the endemic equilibrium point. This model is investigated along with Z-control in order to eliminate chaos and oscillation epidemiologically showing the importance of quarantine in the COVID-19 environment.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2020-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/7876146","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43973422","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: 3
Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations 奇摄动微分-差分方程的指数拟合数值方法
IF 1.6
International Journal of Differential Equations Pub Date : 2020-06-17 DOI: 10.1155/2020/5768323
H. Debela, Solomon Bati Kejela, Ayana Deressa Negassa
{"title":"Exponentially Fitted Numerical Method for Singularly Perturbed Differential-Difference Equations","authors":"H. Debela, Solomon Bati Kejela, Ayana Deressa Negassa","doi":"10.1155/2020/5768323","DOIUrl":"https://doi.org/10.1155/2020/5768323","url":null,"abstract":"This paper presents a numerical method to solve singularly perturbed differential-difference equations. The solution of this problem exhibits layer or oscillatory behavior depending on the sign of the sum of the coefficients in reaction terms. A fourth-order exponentially fitted numerical scheme on uniform mesh is developed. The stability and convergence of the proposed method have been established. The effect of delay parameter (small shift) on the boundary layer(s) has also been analyzed and depicted in graphs. The applicability of the proposed scheme is validated by implementing it on four model examples. Maximum absolute errors in comparison with the other numerical experiments are tabulated to illustrate the proposed method.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"2020 1","pages":"1-13"},"PeriodicalIF":1.6,"publicationDate":"2020-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2020/5768323","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43622640","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
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