摘要：
In this paper, a degenerated reaction-diffusive avian influenza model with logistic source and spatial heterogeneity is proposed. We analyze the global compact attractor of the solution semi-flow of the model using the $ k $-contraction method. Furthermore, the threshold dynamics in terms of the basic reproduction number $ \mathcal{R}_0^{h} $ are investigated. Specifically, if $ \mathcal{R}_0^{h} < 1 $, the infection-free steady state of the system is globally asymptotically stable. If $ \mathcal{R}_0^{h} >1 $, then the endemic equilibrium is uniformly persistent. Finally, numerical simulations are performed to demonstrate the theoretical results.
摘要：
Chemotaxis of mosquito movement has been widely confirmed, but it has rarely been incorporated into infectious disease modeling. This paper proposes a novel mosquito-borne disease model driven by density-suppressed motility and spatial heterogeneity. Via overcoming the difficulties caused by dispersal mechanism and heterogeneity, we establish the global existence and ultimate boundedness of solutions for the model following a priori estimates and the parabolic regularity theory. We define the basic reproduction ratio \(\mathcal {R}_0\) and derive its upper bound \(\tilde {\mathcal {R}}_0\) and lower bound \(\hat {\mathcal {R}}_0\) , and obtain the threshold dynamics of model. Specifically, we prove that the system is uniformly persistent as \(\hat {\mathcal {R}}_0\gt 1\) and the disease will disappear as \(\tilde {\mathcal {R}}_0\lt 1\) by invoking the comparison principle to the corresponding integral system. In the case of spatial homogeneity, the global asymptotic stability of endemic equilibrium is achieved with the aid of a suitable Lyapunov functional and the eigenvalue theory. Numerically, we apply the model to dengue transmission and demonstrate that the chemotaxis of infected mosquitoes may exacerbate the disease in some regions which highlights the impacts of mosquito taxis on the spread of dengue.
期刊：
PROCEEDINGS OF THE 36TH CHINESE CONTROL AND DECISION CONFERENCE, CCDC 2024,2024年:250-253 ISSN：1948-9439
通讯作者：
Yan, R
作者机构：
[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
通讯机构：
[Yan, R ] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
会议名称：
2024 36th Chinese Control and Decision Conference (CCDC)
会议时间：
25 May 2024
会议地点：
Xi'an, China
会议主办单位：
[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.^[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
会议论文集名称：
2024 36th Chinese Control and Decision Conference (CCDC)
关键词：
Fractional boundary value problem;Positive solution;phi-Laplacian operator
摘要：
In this paper, a class of boundary value problems of nonlinear fractional differential equations with phi-Laplacian operator is investigated. Based on the Schauder fixed point theorem, a new existence result for positive solutions, in terms of the value of the parameter h is obtained. Finally, an example is given to illustrate the main result.
期刊：
2024 24TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND SYSTEMS, ICCAS 2024,2024年:1042-1047 ISSN：2093-7121
通讯作者：
Zhao, YG
作者机构：
[Zhao, Yige; Han, Jing] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Zhao, YG ] U;Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
会议名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
会议时间：
29 October 2024
会议地点：
Jeju, Korea, Republic of
会议主办单位：
[Zhao, Yige;Han, Jing] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.^[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
会议论文集名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
关键词：
Fractional boundary value problem;Positive solution;phi-Laplacian operator
摘要：
This paper investigates the existence of positive solutions to boundary value problems for nonlinear fractional differential equations with φ-Laplacian operator, which is fundamental to the study of control theory for such problems. Based on fixed point theorems, several new existence results for positive solutions, in terms of the value of parameters h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>,h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>,h<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> are obtained. Finally, two examples are given to illustrate the main results.
作者机构：
[Shi, Yao] Hebei Univ Engn, Sch Math & Phys, Handan 056038, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.;[Liu, Tao] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Peoples R China.
通讯机构：
[Shi, Y ; Yan, R ] H;Hebei Univ Engn, Sch Math & Phys, Handan 056038, Peoples R China.;Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
摘要：
In this paper, a high-accuracy conservative implicit algorithm for computing the space fractional coupled Schrödinger–Boussinesq system is constructed. Meanwhile, the conservative nature, a priori boundedness, and solvability of the numerical solution are presented. Then, the proposed algorithm is proved to be second-order convergence in temporal and fourth-order spatial convergence using the discrete energy method. Finally, some numerical experiments validate the effectiveness of the conservative algorithm and confirm the accuracy of the theoretical results for different choices of the fractional-order α.
期刊：
Results in Physics,2024年62:107842 ISSN：2211-3797
通讯作者：
Kamsing Nonlaopon
作者机构：
[Fei Long] College of Science, Hunan City University, Yiyang 413000, PR China;[Shami A.M. Alsallami] Department of Mathematical Sciences, College of Applied Science, Umm Al-Qura University, Makkah 21955, Saudi Arabia;[S. Rezaei] Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkey;[Kamsing Nonlaopon] Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand;[E.M. Khalil] Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
通讯机构：
[Kamsing Nonlaopon] D;Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
期刊：
TURKISH JOURNAL OF MATHEMATICS,2024年48(4):645-657 ISSN：1300-0098
通讯作者：
Yan, R
作者机构：
[Leng, Xuan; Yan, Rian; Li, Yabing] Hunan City Univ, Sch Math & Comp Sci, Yiyang, Peoples R China.;[Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan, Peoples R China.
通讯机构：
[Yan, R ] H;Hunan City Univ, Sch Math & Comp Sci, Yiyang, Peoples R China.
关键词：
Caputo fractional derivatives;sign-changing Green's function;fixed point theorem
摘要：
In this paper, Caputo boundary value problems of order 3 < zeta <= 4 are investigated on the interval [0 , 1] . By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green's function changes sign. Finally, two examples are provided to illustrate the application of these results.
期刊：
2024 24TH INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND SYSTEMS, ICCAS 2024,2024年:1048-1053 ISSN：2093-7121
通讯作者：
Zhao, YG
作者机构：
[Li, Yabing; Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.;[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
通讯机构：
[Zhao, YG ] U;Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.
会议名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
会议时间：
29 October 2024
会议地点：
Jeju, Korea, Republic of
会议主办单位：
[Li, Yabing;Zhao, Yige] Univ Jinan, Sch Math Sci, Jinan 250022, Peoples R China.^[Yan, Rian] Hunan City Univ, Sch Math & Comp Sci, Yiyang 413000, Peoples R China.
会议论文集名称：
2024 24th International Conference on Control, Automation and Systems (ICCAS)
关键词：
Variable-order;Existence;Fixed point theorem
摘要：
The existence and uniqueness of solutions of nonlinear fractional differential equations is the key point for stability theory and the design of feedback stabilization controllers. In this paper, we investigate the existence of solutions for initial problems of fractional hybrid differential equations of variable-order 0 < sigma (rho) < 1. Based on the generalized intervals and piecewise constant functions, the existence of solutions is established with the help of a fixed point theorem in the Banach algebra due to Dhage.
作者机构：
[Ding, Qian] Hunan City Univ, Coll Sci, Yiyang 413000, Peoples R China.;[Ding, Qian; Yu, Jianshe; Wang, Kai] Guangzhou Univ, Guangzhou Ctr Appl Math, Guangzhou 510006, Peoples R China.
通讯机构：
[Wang, K ] G;Guangzhou Univ, Guangzhou Ctr Appl Math, Guangzhou 510006, Peoples R China.
关键词：
Fokker-Planck type diffusion;Basic reproduction number;Asymptotic profile;Endemic equilibrium
摘要：
In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker–Planck type diffusion law. The basic reproduction number R 0 of the model is introduced, and the threshold dynamics based on R 0 is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion rate of susceptible individuals approaches zero or infinity.
In this paper, a spatially heterogeneous SIRI epidemic model with general morbidity is studied, which conforms to the Fokker–Planck type diffusion law. The basic reproduction number R 0 of the model is introduced, and the threshold dynamics based on R 0 is discussed. In particular, with the help of elliptic eigenvalue theory, we determine the asymptotic profiles of the endemic equilibrium when the diffusion rate of susceptible individuals approaches zero or infinity.
关键词：
3D Navier-Stokes-Voigt equations;admissible trajectories set;admissible control set;feedback control;time optimal control
摘要：
<jats:p>In this article, we discuss a time optimal feedback control for asymmetrical 3D Navier–Stokes–Voigt equations. Firstly, we consider the existence of the admissible trajectories for the asymmetrical 3D Navier–Stokes–Voigt equations by using the well-known Cesari property and the Fillippove’s theorem. Secondly, we study the existence result of a time optimal control for the feedback control systems. Lastly, asymmetrical Clarke’s subdifferential inclusions and asymmetrical 3D Navier–Stokes–Voigt differential variational inequalities are given to explain our main results.</jats:p>
