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asymptotic behavior of an SIQR epidemic model driven by Lévy jumps on scale-free networks

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International Journal of Biomathematics 2024年第2期17卷 51-86页

作者： Yuncheng Xu Sanyang Liu Xiaojun Sun Hua Hu Yu Wang School of Mathematics and Statistics Xidian University Xi'an 710071P.R.China School of Mathematics and Statistics Ning Xia University Ningria 750021P.R.China School of Mathematics and Information Science Bao Ji University of Arts and Sciences Baoji 721013 P.R.China College of Mathematics Science and Center for Applied Mathematical Science Inner Mongolia Normal University Hohhot 010022 P.R.China

To investigate the effect of information transmission,Levy jumps and contact heterogeneity of individuals on the asymptotic behavior of epidemic,a stochastic SIQR epidemic model with non-monotone incidence rate and Levy jumps on scale-free networks is *** first,the global dynamics of the deterministic model is studied by constructing appropriate Lyapunov *** the stochastic model is made in accordance with the ecological significance,the existence and uniqueness of the global positive solution of the stochastic SIQR model is ***,by constructing suitable stochastic Lyapunov functions and applying Ito formula with jump,the asymptotic behavior of solutions of stochastic model around equilibrium of the corresponding deterministic model is *** last,the correctness of the analytical results is verified by numerical simulations.

关键词： Lévy jumps asymptotic behavior non-monotone incidence rate scale-free networks SIQR.

asymptotic behavior and Nonexistence of Positive Solutions of Delay Difference Equations *L

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Journal of Beijing Institute of Technology 1999年第1期8卷 25-30页

作者：彭名书徐千里北京理工大学应用数学系益阳师范专科学校数学系

Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.

关键词： oscillation asymptotic behavior positive solution neutral delay difference equation nonlinearity

UNIFORM STABILITY AND asymptotic behavior OF SOLUTIONS OF 2-DIMENSIONAL MAGNETOHYDRODYNAMICS EQUATIONS

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Chinese Annals of Mathematics,Series B 1998年第1期19卷 35-58页

作者： ZHANG LINGHAI Department of Mathematics The Ohio State UniversityColumbusOhio43210USA.

This paper is concerned with uniform stability and asymptotic behavior for solutions of 2-dimensional Magnetohydrodynamics equations. The author establishes the corresponding temporal decay estimates when the initial data is in the following Sobolev spaces H 2, L 1∩H 2 with ∫(u 0, A 0)dx≠0, or L 1∩H 2 with ∫(u 0, A 0)dx=0, respectively. Most of the decay rates in these estimates are optimal. Moreover, the author proves various uniform stability results, like  sup t>0 ‖(w, E, r)(t))‖ YC‖(w 0, E 0)‖ X, where X and Y are Sobolev spaces. It should be pointed out that the decay estimates of the solutions for the case (u 0, A 0)∈L 1∩H 2 follow from the uniform stability estimates. The author utilizes the Fourier splitting method invented by Professor Schonbek and the new elaborate global energy estimates.

关键词： Uniform stability asymptotic behavior Magnetohydrodynamics equations Fourier transform Energy estimates

LONG TIME asymptotic behavior OF SOLUTION OF DIFFERENCE SCHEME FOR A SEMILINEAR PARABOLIC EQUATION (Ⅱ)

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Journal of Computational Mathematics 1998年第5期16卷 571-576页

作者： Hui Feng(Shenzhen University Normal College, Shenzhen 518060, China Laboratorp of Computational Physics, Institute of Applied Physics and Computational Mathematics,P.O.Box 8009, Beijing 100088, China )Long-jnn Shen(Laboratory of Computational Physics, In 深圳大学师范学院广东深圳

In this paper we prove the solution of explicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the relevant nonlinear stationary problem as t→∞. For nonlinear parabolic problem, we obtain the long time asymptotic behavior of its discrete solution which is analogous to that of its continuous solution. For simplicity, we discuss one-dimensional problem.

关键词： asymptotic behavior Explicit difference scheme Semilinear parabolic equation.

asymptotic behavior of Positive Solutions of Semilinear Elliptic Equations in R^n, Ⅱ

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Acta Mathematica Sinica,English Series 2010年第9期26卷 1723-1738页

作者： Bai Shun LAI Shu Qing ZHOU Institute of Contemporary Mathematics He 'nan University Kaifeng 475004 P. R. China School of Mathematics and Information Science He 'nan University Kaifeng 475004 P. R. China Department of Mathematics Hu'nan Normal University Changsha 410081 P. R. China

In this paper, we will analyze further to obtain a finer asymptotic behavior of positive solutions of semilinear elliptic equations in R^n by employing the Li＇s method of energy function.

关键词： Semilinear elliptic equation positive solutions asymptotic behavior

Global Existence,asymptotic behavior and Uniform Attractors for Non-autonomous Thermoelastic Systems

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 1015-1034页

作者： Yu-ming QIN Tian-hui WEI Jia REN Department of Applied Mathematics Donghua University

In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.

关键词： Thermoelastic systems global existence asymptotic behavior uniform attractors semigroupmethods

asymptotic behavior of Product of Two Heavy-tailed Dependent Random Variables

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Acta Mathematica Sinica,English Series 2013年第2期29卷 355-364页

作者： Vahid RANJBAR Mohammad AMINI Jaap GELUK Abolghasem BOZORGNIA Department of Statistics Faculty of SciencesGolestan University Department of Statistics Ordered and Spatial Data Center of ExcellenceFerdowsi University of Mashhad Department of Mathematics The Petroleum Institute

Let X and Y be positive weakly negatively dependent （WND） random variables with finite expectations and continuous distribution functions F and G with heavy tails, respectively. The asymptotic behavior of the tail of distribution of XY is studied and some closure properties under some suitable conditions on F（x） = 1-F（x） and G（x） = of XY when X and Y are WND random variables 1- G（x） are provided. Moreover, subexponentiality is derived.

关键词： Weakly negative dependent heavy-tailed asymptotic behavior

asymptotic behavior TOWARD THE RAREFACTION WAVE FOR SOLUTIONS OF RATE-TYPE VISCOELASTIC SYSTEM WITH BOUNDARY EFFECT

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Acta Mathematica Scientia 2000年第2期20卷 245-255页

作者：何成李海梁 Institute of Mathematics Academia Sinica Beijing 100080 China

The initial boundary value problems for the system of rate-type viscoelasticityis considered in the present *** is shown that if the initial data are a small perturbationof a forward smooth rarefaction wave, then ther... 详细信息

关键词： Initial boundary value problems relaxation global existence asymptotic behavior

asymptotic behavior of the principal eigenvalue and the basic reproduction ratio for periodic patch models

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Science China Mathematics 2022年第7期65卷 1363-1382页

作者： Lei Zhang Xiao-Qiang Zhao Department of Mathematics Harbin Institute of Technology at WeihaiWeihai 264209China Department of Mathematics and Statistics Memorial University of NewfoundlandSt.John'sNL A1C 5S7Canada

This paper is devoted to the study of the asymptotic behavior of the principal eigenvalue and the basic reproduction ratio associated with periodic population models in a patchy environment for small and large dispersal *** first deal with the eigenspace corresponding to the zero eigenvalue of the connectivity *** we investigate the limiting profile of the principal eigenvalue of an associated periodic eigenvalue problem as the dispersal rate goes to zero and infinity,*** further establish the asymptotic behavior of the basic reproduction ratio in the case of small and large dispersal ***,we apply these results to a periodic Ross-Macdonald patch model.

关键词： asymptotic behavior periodic systems patchy environment basic reproduction ratio principal eigenvalue