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A novel approach to find analytical solutions for Oldroyd 6-constant fluid 一种寻找Oldroyd 6常流体解析解的新方法
Nonlinear Analysis and Differential Equations Pub Date : 2023-01-01 DOI: 10.12988/nade.2023.91144
M. Hameed, S. Boebel
{"title":"A novel approach to find analytical solutions for Oldroyd 6-constant fluid","authors":"M. Hameed, S. Boebel","doi":"10.12988/nade.2023.91144","DOIUrl":"https://doi.org/10.12988/nade.2023.91144","url":null,"abstract":"The study is concerned with the application of a novel idea used to find analytical solutions of a nonlinear boundary value problem that arises in channel flow problems. The velocity profile of a viscoelastic fluid between two planes is obtained with both slip and no-slip boundary conditions. We present analytical solutions on classical problems – the Poiseuille flow, and the generalized Couette flow of a viscoelastic fluid between two parallel planes. The viscoelastic fluid is modeled by an Oldroyd 6-constant fluid, giving rise to a highly nonlinear ordinary differential equation. This equation has been solved via a novel approach by reducing the differential equation to a cubic algebraic equation, giving rise to a non-recursive series solution to the equation. Finally, after the solution of the general differential equation is given Newton’s Method is used for faster convergence to solve the equation in the case of three common boundary conditions.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135010461","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 system of inverted nonsmooth pendula: modelling an elderly person stepping over an obstacle 一个倒置的非光滑钟摆系统:模拟一个老人跨过障碍
Nonlinear Analysis and Differential Equations Pub Date : 2019-04-26 DOI: 10.12988/NADE.2019.934
P. Stiefenhofer, P. Giesl, H. Wagner
{"title":"A system of inverted nonsmooth pendula: modelling an elderly person stepping over an obstacle","authors":"P. Stiefenhofer, P. Giesl, H. Wagner","doi":"10.12988/NADE.2019.934","DOIUrl":"https://doi.org/10.12988/NADE.2019.934","url":null,"abstract":"We derive a mechanical model of human motion where an elderly person decides to step over an obstacle rather than avoiding it. Such a decision may be deliberate or \u0000forced due to a sudden appearing obstacle in his/her way. The model is represented by a nonautonomous system of ordinary differential equations with discontinuous right hand side. We provide a notion of lateral stability. It is shown that increasing the angle between legs increases stability linearly. This implies that an individual reduces the risk of falling due to stepping over an obstacle by increasing the angle between legs.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130396489","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
Economic periodic orbits: a theory of exponential asymptotic stability 经济周期轨道:指数渐近稳定性理论
Nonlinear Analysis and Differential Equations Pub Date : 2019-04-11 DOI: 10.12988/NADE.2019.923
P. Stiefenhofer, P. Giesl
{"title":"Economic periodic orbits: a theory of exponential asymptotic stability","authors":"P. Stiefenhofer, P. Giesl","doi":"10.12988/NADE.2019.923","DOIUrl":"https://doi.org/10.12988/NADE.2019.923","url":null,"abstract":"This paper establishes the conditions for existence, uniqueness, and exponentially asymptotically stability of periodic orbits of a dynamical system defined by a set of ordinary differential equations with discontinuous right-hand side. Moreover, a formula for the basin of attraction is provided. These results equip economists with a set of tools, which will allow them to generate new analytic results.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123563180","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
Coefficient estimates for some subclasses of bi-univalent functions 双一元函数某些子类的系数估计
Nonlinear Analysis and Differential Equations Pub Date : 2017-04-27 DOI: 10.1063/1.4980967
Andy Liew Pik Hern, A. Janteng
{"title":"Coefficient estimates for some subclasses of bi-univalent functions","authors":"Andy Liew Pik Hern, A. Janteng","doi":"10.1063/1.4980967","DOIUrl":"https://doi.org/10.1063/1.4980967","url":null,"abstract":"Let A be a class of functions of the form f(z)=z+∑n=2∞anzn which are analytic in the open unit disc D={ z∈ℂ:| z |<1 } where an is a complex number. Also let S denotes a subclass of all functions in A which are univalent in D and let Σ denotes the class of bi-univalent functions in D. In this paper, we introduce two subclasses of Σ defined in the open unit disk D which are denoted by G∑s(α,β) and G*∑s(α,β) and we find the upper bounds for the second and S LS third coefficients for functions in these subclasses.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128271073","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
Investigation of non-lightlike tubular surfaces with Darboux frame in Minkowski 3-space Minkowski三维空间中具有Darboux框架的非光状管状表面的研究
Nonlinear Analysis and Differential Equations Pub Date : 2016-06-01 DOI: 10.12988/NADE.2016.6752
E. Solouma
{"title":"Investigation of non-lightlike tubular surfaces with Darboux frame in Minkowski 3-space","authors":"E. Solouma","doi":"10.12988/NADE.2016.6752","DOIUrl":"https://doi.org/10.12988/NADE.2016.6752","url":null,"abstract":"In this paper, the spacelike tubular surface with Darboux frame is introduced in Minkowski 3-space E 1 3 . Then, some characterizations were investigated for special curves on this tube with Darboux frame in Minkowski 3-space. Finally, we compute the  Gaussian and mean curvature of tubular surface with Darboux frame.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"235 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121040863","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
Sobolev-Il'in inequality for a class of generalized shift subadditive operators 一类广义移位次加性算子的Sobolev-Il'in不等式
Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI: 10.12988/NADE.2017.61299
S. K. Abdullayev, E. A. Mammadov
{"title":"Sobolev-Il'in inequality for a class of generalized shift subadditive operators","authors":"S. K. Abdullayev, E. A. Mammadov","doi":"10.12988/NADE.2017.61299","DOIUrl":"https://doi.org/10.12988/NADE.2017.61299","url":null,"abstract":"We study a problem of establishment of Sobolev-Il’in inequalities type strong and weak inequalities for subadditive operators with majorizing operators from certain class of Riesz potential type integral convolutions with almost monotone kernels, generated by both ordinary and generalized shift operators, associated with Laplace-Bessel differential operator.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127221900","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
Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions 非标准增长条件下标量积分泛函局部极小值的连续性
Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI: 10.12988/NADE.2015.4711
Tiziano Granucci
{"title":"Remarks on the continuity of the local minimizer of scalar integral functionals with nonstandard growth conditions","authors":"Tiziano Granucci","doi":"10.12988/NADE.2015.4711","DOIUrl":"https://doi.org/10.12988/NADE.2015.4711","url":null,"abstract":"In this paper we show a regularity theorem for quasi-minima of scalar integral functionals of the Calculus of Variations with nonstandard growth conditions. Let us consider functionals as the following form","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124948179","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
Global Strong Solution to a Nonlinear Dispersive Wave Equation 一类非线性色散波动方程的全局强解
Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI: 10.12988/NADE.2013.13005
Yunxi Guo, Ying Wang
{"title":"Global Strong Solution to a Nonlinear Dispersive Wave Equation","authors":"Yunxi Guo, Ying Wang","doi":"10.12988/NADE.2013.13005","DOIUrl":"https://doi.org/10.12988/NADE.2013.13005","url":null,"abstract":"In this paper, compared with the previous results, a new global existence for strong solutions to the equation is acquired provided that the potential (1−∂ 2 )u0 changes sign on R, which improves considerably the previous result.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125958928","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 mathematical model to assess the effect of the constant release policy on population suppression 定量放生政策对种群抑制效果的数学模型
Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI: 10.12988/NADE.2017.735
Bo Zheng, Yugeng Xiao
{"title":"A mathematical model to assess the effect of the constant release policy on population suppression","authors":"Bo Zheng, Yugeng Xiao","doi":"10.12988/NADE.2017.735","DOIUrl":"https://doi.org/10.12988/NADE.2017.735","url":null,"abstract":"In this paper, we developed a mathematical model to assess the effect of the constant release policy on population suppression. We found a threshold value of the number of infected males released to guarantee the successful population suppression, above which the wild mosquito population will be eradicated, and below which the wild population will outcompete the released males. Mathematics Subject Classification: 92B05, 37N25, 34D23, 92D30","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125534863","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
Solutions of first and second order power quantum difference equations 一阶和二阶幂量子差分方程的解
Nonlinear Analysis and Differential Equations Pub Date : 1900-01-01 DOI: 10.12988/NADE.2016.511274
M. Al-Ashwal, K. Aldwoah, A. Hamza
{"title":"Solutions of first and second order power quantum difference equations","authors":"M. Al-Ashwal, K. Aldwoah, A. Hamza","doi":"10.12988/NADE.2016.511274","DOIUrl":"https://doi.org/10.12988/NADE.2016.511274","url":null,"abstract":"Abstract Jackson in 1908 introduced the most well–known and used quantum difference operator Dqf(t) = (f(qt)−f(t))/(qt−t) for a fixed 0 < q < 1. Aldwoah in 2009 [3], introduced the power quantum n, q–difference operator Dn,qf(t) = (f(qt n) − f(t))/(qtn − t), where n is an odd natural number and q ∈ (0, 1) are fixed. Dn,q yields Jackson q–difference operator, when n = 1. In this paper, we define the n, q–exponential and n, q–trigonometric (hyperbolic) functions and we establish some of their properties. We prove that they are solutions of power quantum difference equations of first and second order respectively.","PeriodicalId":315586,"journal":{"name":"Nonlinear Analysis and Differential Equations","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126775480","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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