Pub Date : 2022-12-23DOI: 10.15388/namc.2023.28.29621
Wenwen Hou, Lihong Zhang
In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the relativistic Schrödinger operator (–Δ + m2)s and the tempered fractional Laplacian (Δ + λ)β/2, we consider a relativistic Schrödinger tempered fractional p-Laplacian model involving logarithmic nonlinearity. We first establish maximum principle and boundary estimate, which play a very crucial role in the later process. Then we obtain radial symmetry and monotonicity results by using the direct method of moving planes.
{"title":"Radial symmetry of a relativistic Schrödinger tempered fractional p-Laplacian model with logarithmic nonlinearity","authors":"Wenwen Hou, Lihong Zhang","doi":"10.15388/namc.2023.28.29621","DOIUrl":"https://doi.org/10.15388/namc.2023.28.29621","url":null,"abstract":"In this paper, by introducing a relativistic Schrödinger tempered fractional p-Laplacian operator (–Δ)p,λs,m, based on the relativistic Schrödinger operator (–Δ + m2)s and the tempered fractional Laplacian (Δ + λ)β/2, we consider a relativistic Schrödinger tempered fractional p-Laplacian model involving logarithmic nonlinearity. We first establish maximum principle and boundary estimate, which play a very crucial role in the later process. Then we obtain radial symmetry and monotonicity results by using the direct method of moving planes.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46354470","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}
Pub Date : 2022-12-23DOI: 10.15388/namc.2023.28.29734
Ayse Nur Altunkaya, O. Aydin, M. Avci
In this study, the pulsating flow of a non-Newtonian fluid and heat transfer in a pipe with uniform heat flux at its wall is examined analytically. The flow is assumed to be both hydrodynamically and thermally fully developed. The perturbation method based on the series expansion is used in the analysis. The periodic change and period-averaged values of the friction factor and Nusselt number as well as velocity and temperature profiles are obtained at varying values of dimensionless frequency and amplitude for shear-thinning, Newtonian and shear-thickening fluids. It is shown that the frequency is effective on the friction factor for a specific range of the dimensionless frequency. For some specific cases, excellent agreements are obtained with the literature. It is disclosed that the dimensionless frequency, the amplitude and the power-law index are interactively effective on the friction and heat transfer.
{"title":"Pulsating flow and heat transfer of power-law fluid in a circular pipe","authors":"Ayse Nur Altunkaya, O. Aydin, M. Avci","doi":"10.15388/namc.2023.28.29734","DOIUrl":"https://doi.org/10.15388/namc.2023.28.29734","url":null,"abstract":"In this study, the pulsating flow of a non-Newtonian fluid and heat transfer in a pipe with uniform heat flux at its wall is examined analytically. The flow is assumed to be both hydrodynamically and thermally fully developed. The perturbation method based on the series expansion is used in the analysis. The periodic change and period-averaged values of the friction factor and Nusselt number as well as velocity and temperature profiles are obtained at varying values of dimensionless frequency and amplitude for shear-thinning, Newtonian and shear-thickening fluids. It is shown that the frequency is effective on the friction factor for a specific range of the dimensionless frequency. For some specific cases, excellent agreements are obtained with the literature. It is disclosed that the dimensionless frequency, the amplitude and the power-law index are interactively effective on the friction and heat transfer.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44901580","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}
Pub Date : 2022-12-23DOI: 10.15388/namc.2023.28.29622
Lei Shi, Rongqiang Tang, Xinsong Yang, Jiaxuan Ding, Zhilu Xu, Yingchun Li
It is well known that designing mode-dependent event-triggered control (MDETC) brings challenging difficulties to theoretical analysis, especially for two-dimensional (2-D) switched systems. Therefore, for 2-D switched Fornasini–Marchesini local state-space (FMLSS) systems, this paper designs a MDETC to investigate global exponential stabilization almost surely (GES a.s.). A MDETC based on dynamic output quantization control scheme is designed, which not only has a wide range of practicability, but also greatly saves network bandwidth resources. By constructing mode-dependent Lyapunov functions that include two time directions, some novel sufficient conditions are provided such that the switched FMLSS system achieves GES a.s. Unlike most previous results, our results do not require each mode to be stable, not even after adding control. Finally, numerical experiments are provided to verify the validity of our main theoretical results.
{"title":"Event-triggered dynamic output quantized control for 2-D switched systems","authors":"Lei Shi, Rongqiang Tang, Xinsong Yang, Jiaxuan Ding, Zhilu Xu, Yingchun Li","doi":"10.15388/namc.2023.28.29622","DOIUrl":"https://doi.org/10.15388/namc.2023.28.29622","url":null,"abstract":"It is well known that designing mode-dependent event-triggered control (MDETC) brings challenging difficulties to theoretical analysis, especially for two-dimensional (2-D) switched systems. Therefore, for 2-D switched Fornasini–Marchesini local state-space (FMLSS) systems, this paper designs a MDETC to investigate global exponential stabilization almost surely (GES a.s.). A MDETC based on dynamic output quantization control scheme is designed, which not only has a wide range of practicability, but also greatly saves network bandwidth resources. By constructing mode-dependent Lyapunov functions that include two time directions, some novel sufficient conditions are provided such that the switched FMLSS system achieves GES a.s. Unlike most previous results, our results do not require each mode to be stable, not even after adding control. Finally, numerical experiments are provided to verify the validity of our main theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45825194","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}
Pub Date : 2022-12-23DOI: 10.15388/namc.2023.28.30208
D. Konstantinides, R. Leipus, J. Šiaulys
In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution.
{"title":"On the non-closure under convolution for strong subexponential distributions","authors":"D. Konstantinides, R. Leipus, J. Šiaulys","doi":"10.15388/namc.2023.28.30208","DOIUrl":"https://doi.org/10.15388/namc.2023.28.30208","url":null,"abstract":"In this paper, we consider the convolution closure problem for the class of strong subexponential distributions, denoted as S*. First, we show that, if F, G ∈ L, then inclusions of F*G, FG, and pF + (1 – p)G for all (some) p ∈ (0; 1) into the class S* are equivalent. Then, using examples constructed by Klüppelberg and Villasenor [The full solution of the convolution closure problem for convolution-equivalent distributions, J. Math. Anal. Appl., 41:79–92, 1991], we show that S* is not closed under convolution.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48548326","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}
Pub Date : 2022-11-22DOI: 10.15388/namc.2023.28.29615
Liru Zhang
In this paper, we propose an HIV model with latent reservoir, delayed CTL immune response and immune impairment in which both virus-to-cell infection and cell-to-cell viral transmission are considered. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that when time delay is equal to zero, the global threshold dynamics of the model is determined by the basic reproduction ratio. With the help of uniform persistence theory for infinite dimensional systems, we obtain the uniform persistence when the basic reproduction ratio is greater than unity. By choosing time delay as a bifurcation parameter and analyzing the corresponding characteristic equation of the system, we establish the existence of Hopf bifurcation at the chronic-infection equilibrium. Numerical simulations are carried out to illustrate the corresponding theoretical results.
{"title":"Dynamics analysis of an HIV infection model with latent reservoir, delayed CTL immune response and immune impairment","authors":"Liru Zhang","doi":"10.15388/namc.2023.28.29615","DOIUrl":"https://doi.org/10.15388/namc.2023.28.29615","url":null,"abstract":"In this paper, we propose an HIV model with latent reservoir, delayed CTL immune response and immune impairment in which both virus-to-cell infection and cell-to-cell viral transmission are considered. By using Lyapunov functionals and LaSalle’s invariance principle, it is verified that when time delay is equal to zero, the global threshold dynamics of the model is determined by the basic reproduction ratio. With the help of uniform persistence theory for infinite dimensional systems, we obtain the uniform persistence when the basic reproduction ratio is greater than unity. By choosing time delay as a bifurcation parameter and analyzing the corresponding characteristic equation of the system, we establish the existence of Hopf bifurcation at the chronic-infection equilibrium. Numerical simulations are carried out to illustrate the corresponding theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":"48 1","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80610109","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}
Pub Date : 2022-10-19DOI: 10.15388/namc.2022.27.29503
Wenxia Wang
This paper investigates the existence of a unique positive solution for a class of boundary value problems of p-Laplacian fractional differential equations, where its nonlinearity is signchanged and involves a fractional derivative term, and its boundary involves a nonlinear fractional integral term. By constructing an appropriate auxiliary boundary value problem and applying a generalized fixed point theorem of sum operator and properties of Mittag-Leffler function, some sufficient conditions for the existence of a unique positive solution are presented, and a monotone iterative sequence uniformly converging to the unique solution is constructed. In addition, an example is given to illustrate the main result.
{"title":"Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity","authors":"Wenxia Wang","doi":"10.15388/namc.2022.27.29503","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29503","url":null,"abstract":"This paper investigates the existence of a unique positive solution for a class of boundary value problems of p-Laplacian fractional differential equations, where its nonlinearity is signchanged and involves a fractional derivative term, and its boundary involves a nonlinear fractional integral term. By constructing an appropriate auxiliary boundary value problem and applying a generalized fixed point theorem of sum operator and properties of Mittag-Leffler function, some sufficient conditions for the existence of a unique positive solution are presented, and a monotone iterative sequence uniformly converging to the unique solution is constructed. In addition, an example is given to illustrate the main result.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45984899","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}
Pub Date : 2022-10-19DOI: 10.15388/namc.2022.27.29420
Weiwei Liu, Lishan Liu
This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.
{"title":"Existence and stability analysis of solutions for a new kind of boundary value problems of nonlinear fractional differential equations","authors":"Weiwei Liu, Lishan Liu","doi":"10.15388/namc.2022.27.29420","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29420","url":null,"abstract":"This research work is dedicated to an investigation for a new kind of boundary value problem of nonlinear fractional differential equation supplemented with general boundary condition. A full analysis of existence and uniqueness of positive solutions is respectively proved by Leray–Schauder nonlinear alternative theorem and Boyd–Wong’s contraction principles. Furthermore, we prove the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of solutions. An example illustrating the validity of the existence result is also discussed.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45997042","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}
Pub Date : 2022-10-19DOI: 10.15388/namc.2022.27.29471
Xue Li, Zhiyong Yu, Da Huang, Haijun Jiang
In this paper, the leader-following consensus of second-order nonlinear multiagent systems (SONMASs) with external disturbances is studied. Firstly, based on terminal sliding model control method, a distributed control protocol is proposed over undirected networks, which can not only suppress the external disturbances, but also make the SONMASs achieve consensus in finite time. Secondly, to make the settling time independent of the initial values of systems, we improve the protocol and ensure that the SONMASs can reach the sliding surface and achieve consensus in fixed time if the control parameters satisfy some conditions. Moreover, for general directed networks, we design a new fixed-time control protocol and prove that both the sliding mode surface and consensus for SONMASs can be reached in fixed time. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.
{"title":"Finite-time and fixed-time sliding mode control for second-order nonlinear multiagent systems with external disturbances","authors":"Xue Li, Zhiyong Yu, Da Huang, Haijun Jiang","doi":"10.15388/namc.2022.27.29471","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29471","url":null,"abstract":"In this paper, the leader-following consensus of second-order nonlinear multiagent systems (SONMASs) with external disturbances is studied. Firstly, based on terminal sliding model control method, a distributed control protocol is proposed over undirected networks, which can not only suppress the external disturbances, but also make the SONMASs achieve consensus in finite time. Secondly, to make the settling time independent of the initial values of systems, we improve the protocol and ensure that the SONMASs can reach the sliding surface and achieve consensus in fixed time if the control parameters satisfy some conditions. Moreover, for general directed networks, we design a new fixed-time control protocol and prove that both the sliding mode surface and consensus for SONMASs can be reached in fixed time. Finally, several numerical simulations are given to show the effectiveness of the proposed protocols.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49580281","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}
Pub Date : 2022-10-19DOI: 10.15388/namc.2022.27.29533
I. Zamaraite, S. Rudys, S. Lapinskas, R. Aleksiejūnas, R. Grigalaitis, J. Banys
In this paper, the full-wave analysis of the direct scattering problem in the rectangular waveguide is derived. The numerical calculation results of the scattering characteristics are presented. To show the advantage of our proposed model, we compared direct problem results with three-dimensional simulation software Ansys HFSS calculations. An excellent agreement is observed when compared these two approaches.
{"title":"Computational electromagnetic analysis of partially-filled rectangular waveguide at X-band frequencies","authors":"I. Zamaraite, S. Rudys, S. Lapinskas, R. Aleksiejūnas, R. Grigalaitis, J. Banys","doi":"10.15388/namc.2022.27.29533","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29533","url":null,"abstract":"In this paper, the full-wave analysis of the direct scattering problem in the rectangular waveguide is derived. The numerical calculation results of the scattering characteristics are presented. To show the advantage of our proposed model, we compared direct problem results with three-dimensional simulation software Ansys HFSS calculations. An excellent agreement is observed when compared these two approaches.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48688994","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}
Pub Date : 2022-10-19DOI: 10.15388/namc.2022.27.29535
Xiao Wu, Mingkang Ni
This paper is concerned with the diffusive Leslie–Gower prey–predator model with weak diffusion. Assuming that the diffusion rates of prey and predator are sufficiently small and the natural growth rate of prey is much greater than that of predators, the diffusive Leslie–Gower prey–predator model is a singularly perturbed problem. Using travelling wave transformation, we firstly transform our problem into a multiscale slow-fast system with two small parameters. We prove the existence of heteroclinic orbit, canard explosion phenomenon and relaxation oscillation cycle for the slow-fast system by applying the geometric singular perturbation theory. Thus, we get the existence of travelling waves and periodic solutions of the original reaction–diffusion model. Furthermore, we also give some numerical examples to illustrate our theoretical results.
{"title":"Dynamics in diffusive Leslie–Gower prey–predator model with weak diffusion","authors":"Xiao Wu, Mingkang Ni","doi":"10.15388/namc.2022.27.29535","DOIUrl":"https://doi.org/10.15388/namc.2022.27.29535","url":null,"abstract":"This paper is concerned with the diffusive Leslie–Gower prey–predator model with weak diffusion. Assuming that the diffusion rates of prey and predator are sufficiently small and the natural growth rate of prey is much greater than that of predators, the diffusive Leslie–Gower prey–predator model is a singularly perturbed problem. Using travelling wave transformation, we firstly transform our problem into a multiscale slow-fast system with two small parameters. We prove the existence of heteroclinic orbit, canard explosion phenomenon and relaxation oscillation cycle for the slow-fast system by applying the geometric singular perturbation theory. Thus, we get the existence of travelling waves and periodic solutions of the original reaction–diffusion model. Furthermore, we also give some numerical examples to illustrate our theoretical results.","PeriodicalId":49286,"journal":{"name":"Nonlinear Analysis-Modelling and Control","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48281685","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：