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traveling waves IN A SIRH MODEL WITH SPATIO-TEMPORAL DELAY AND NONLOCAL DISPERSAL

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Acta Mathematica Scientia 2022年第2期42卷 715-736页

作者： Lu YANG Yun-Rui YANG Xue SONG School of Mathematics and Physics Lanzhou Jiaotong UniversityLanzhou 730070China

This paper deals mainly with the existence and asymptotic behavior of traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal based on Schauder’s fixed-point theorem and analysis techniques,which generalize the results of nonlocal SIRH models without relapse and *** particular,the difficulty of obtaining the asymptotic behavior of traveling waves for the appearance of spatio-temporal delay is overcome by the use of integral techniques and analysis ***,the more general nonexistence result of traveling waves is also included.

关键词： Nonlocal dispersal spatio-temporal delay traveling waves

traveling waves of a delayed HIV/AIDS epidemic model with treatment and spatial diffusion

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International Journal of Biomathematics 2021年第3期14卷 121-151页

作者： Qintao Gan Rui Xu Jing Yang Shijiazhuang Campus Army Engineering University ShijiazhuangHebei 050003P.R.China Complex Systems Research Center Shanxi University TaiyuanShanxi 030006P.R.China

In this paper,a delayed HIV/AIDS epidemic model with treatment and spatial diffusion is *** analyzing the corresponding characteristic equations,the local stability of a disease-free steady state and an endemic steady state is *** using the cross-iteration method and Schauder’s fixed point theorem,we reduce the existence of traveling waves to the existence of a pair of upper-lower *** constructing a pair of upper-lower solutions,we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady *** is shown that the existence of traveling waves of the proposed HIV/AIDS epidemic model is fully determined by the basic reproduction number and the minimal wave ***,numerical simulations are performed to show the feasibility and effectiveness of the theoretical results.

关键词： HIV/AIDS reaction-diffusion traveling waves upper-lower solutions partial monotonicity

The Stability of traveling waves with Non-critical Speeds for Some Competition Systems

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Acta Mathematicae Applicatae Sinica 2010年第4期26卷 643-652页

作者： Ye Zhao Department of Mathematics and Physics Beijing Institute of Petrolchemical-TechnologyBeijing 102617China

This paper is concerned with some quasilinear cross-diffusion systems which model competing species in mathematical *** detailed spectral analysis,each traveling wave solution with non-critical speed is proved to be l... 详细信息

关键词： traveling waves asymptotic stability spectral analysis

ON MONOTONE traveling waves FOR NICHOLSON'S BLOWFLIES EQUATION WITH DEGENERATE p-LAPLACIAN DIFFUSION

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Acta Mathematica Scientia 2024年第4期44卷 1550-1571页

作者： Rui HUANG Yong WANG Zhuo YIN School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian *** prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis ***,we show the existence and regularity of an original solution via a compactness ***,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.

关键词： degenerate diffusion p-Laplacian traveling waves stability

STABILITY OF traveling waves IN A POPULATION DYNAMIC MODEL WITH DELAY AND QUIESCENT STAGE

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Acta Mathematica Scientia 2018年第3期38卷 1001-1024页

作者： Yonghui ZHOU Yunrui YANG Kepan LIU School of Mathematics and Physics Lanzhou Jiaotong Universit

This article is concerned with a population dynamic model with delay and quiescent stage. By using the weighted-energy method combining continuation method, the exponential stability of traveling waves of the model under non-quasi-monotonicity conditions is established. Particularly, the requirement for initial perturbation is weaker and it is uniformly bounded only at x = ＋∞ but may not be vanishing.

关键词： Stability traveling waves weighted-energy method

traveling waves in Degenerate Diffusion Equations

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Communications in Mathematical Research 2023年第1期39卷 36-53页

作者： Tianyuan Xu Jingxue Yin School of Mathematics South China University of TechnologyGuangzhou 510641P.R.China School of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this survey,we present a literature review on the study of travel-ing waves in degenerate diffusion equations by illustrating the interesting and singular wave behavior caused by *** main results on wave exis-tence and stability are presented for the typical degenerate equations,including porous medium equations,flux limited diffusion equations,delayed degener-ate diffusion equations,and other strong degenerate diffusion equations.

关键词： traveling waves degenerate diffusion equation existence stability

traveling waves FOR A NONLOCAL DISPERSAL EPIDEMIC MODEL

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Annals of Differential Equations 2014年第2期30卷 222-235页

作者： Feiying Yang Runlong Qiao Wantong Li School of Math.and Statistics Lanzhou University

This paper is concerned with traveling wave solutions to a nonlocal dispersal epide- mic model. Combining the upper and lower solutions and monotone iteration method, we establish the existence of nondecreasing traveling wave fronts for the speed being larger than the critical one. Furthermore, by the approximation method, the existence of traveling wave fronts for the critical speed is established as well. Finally, we discuss the nonexistence of traveling wave fronts for the speed being smaller than critical one by Laplace transform.

关键词： traveling waves nonlocal dispersal Laplace transform

Fault location method for transmission line based on traveling waves

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Journal of Northeast Agricultural University(English Edition) 2007年第1期14卷 79-81页

作者： ZHENG Na ZHAO Yulin College of Electronic Message Beihua University Jilin 132021 China Engineering College Northeast Agricultural University Harbin 150030 China

The single phase grounding fault location is the focus which researchers pay attention to and study in power system. The accurate fault location can lighten the patrolling burden, and enhance the reliability of the power network. It adopts A/D which has high speed, and uses TMS320VC5402 DSP chip as the system core. This paper presented theory of operation based on traveling waves and achieved software and hardware in detail.

关键词： traveling waves fault location DSP

traveling waves for 2-1 Dimension Lattice Difference Equations

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Chinese Quarterly Journal of Mathematics 2013年第2期28卷 214-223页

作者： HE Yan-sheng HOU Cheng-min Department of Mathematics Yanbian University Yanji 133002 China

A definition is introduced about traveling waves of 2-1 dimension lattice difference equations. Discrete heat equation is introduced and a discussion is given for the existence of traveling waves. The theory of traveling waves is extended on 2-1 dimension lattice difference equations. As an application, an example is presented to illustrate the main results.

关键词： traveling waves lattice difference equations discrete heat equation