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DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY

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Acta Mathematica Scientia 2024年第3期44卷 1046-1063页

作者：涂馨予穆春来邱蜀燕张静 School of Mathematics and Statistics Southwest UniversityChongqing400715China Department of Applied Mathematics The Hong Kong Polytechnic UniversityHung HomHong KongChina College of Mathematics and Statistics Chongqing UniversityChongqing401331China School of Sciences Southwest Petroleum UniversityChengdu610500China

In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).

关键词： chemotaxis signal-dependent motility logistic source boundedness asymptotic behavior

Synchronization of Drive-Response Networks With Delays on Time Scales

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IEEE/CAA Journal of Automatica Sinica 2024年第4期11卷 1063-1065页

作者： Yanxia Tan Zhenkun Huang the School of Science Jimei UniversityXiamen 361021China

Dear Editor,This letter deals with the synchronization in drive-response networks with discrete and distributed delays on time scales.Based on the theory of calculus on time scales,Lyapunov functional method and inequality technique,we obtain new sufficient conditions to ensure synchronization criteria which are dependent on boundedness of grainness but independent of the types of delays.Numerical simulations are given to illustrate the effectiveness of our new results.

关键词： inequality letter boundedness

boundedness of Solutions of Quasi-periodic p-Laplacian Equations with Jumping Nonlinearity

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Acta Mathematica Sinica,English Series 2023年第1期39卷 176-192页

作者： Xin Li ZHANG Ya Qun PENG Da Xiong PIAO School of Mathematics and Physics Qingdao University of Science and TechnologyQingdao 266061P.R.China School of Mathematics(Zhuhai) Sun Yat-sen UniversityZhuhai 519082P.R.China School of Mathematical Sciences Ocean University of ChinaQingdao 266100P.R.China

In this article,we prove the existence of quasi-periodic solutions and the boundedness of all solutions of the p-Laplacian equation(φ_(p)(x’))’+aφ_(p)(x+)-bφ_(p)(x-)=g(x,t)+f(t),where g(x,t)and f(t)are quasi-periodic in t with Diophantine frequency.A new method is presented to obtain the generating function to construct canonical transformation by solving a quasi-periodic homological equation.

关键词： Quasi-periodic twist mapping invariant curve boundedness p-Laplacian

boundedness AND EXPONENTIAL STABILIZATION IN A PARABOLIC-ELLIPTIC KELLER–SEGEL MODEL WITH SIGNAL-DEPENDENT MOTILITIES FOR LOCAL SENSING CHEMOTAXIS

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Acta Mathematica Scientia 2022年第3期42卷 825-846页

作者：江杰 Innovation Academy for Precision Measurement Science and Technology CASWuhan 430071China

In this paper we consider the initial Neumann boundary value problem for a degenerate Keller-Segel model which features a signal-dependent non-increasing motility function.The main obstacle of analysis comes from the possible degeneracy when the signal concentration becomes unbounded.In the current work,we are interested in the boundedness and exponential stability of the classical solution in higher dimensions.With the aid of a Lyapunov functional and a delicate Alikakos-Moser type iteration,we are able to establish a time-independent upper bound of the concentration provided that the motility function decreases algebraically.Then we further prove the uniform-in-time boundedness of the solution by constructing an estimation involving a weighted energy.Finally,thanks to the Lyapunov functional again,we prove the exponential stabilization toward the spatially homogeneous steady states.Our boundedness result improves those in[1]and the exponential stabilization is obtained for the first time.

关键词： Classical solution boundedness exponential stabilization degeneracy Keller-Segel models

boundedness AND ASYMPTOTIC STABILITY IN A PREDATOR-PREY CHEMOTAXIS SYSTEM WITH INDIRECT PURSUIT-EVASION DYNAMICS

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Acta Mathematica Scientia 2022年第3期42卷 1035-1057页

作者：邱蜀燕穆春来易红 School of Sciences Southwest Petroleum UniversityChengdu 610500China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China School of Mathematics and Statistics Chongqing Technology and Business UniversityChongqing 400067China

This work explores the predator-prey chemotaxis system with two chemicals {u_(t) = Δu + ∇ ・ (u∇v) + μ_(1)u(1 − u − α_(1)w), x ∈ Ω, t > 0,v_(t )= Δv −α_(1)v + β_(1)w, x ∈ Ω, t > 0,w_(t) = Δw − ξ∇ ・ (w∇z) + μ_(2)w(1 + α_(2)u − w), x ∈ Ω, t > 0,z_(t) =Δz −α_(2)z +β_(2)u, x ∈ Ω, t > 0, in an arbitrary smooth bounded domainΩ■R^(n) under homogeneous Neumann boundary conditions.The parameters in the system are positive.We first prove that if n≤3,the corresponding initial-boundary value problem admits a unique global bounded classical solution,under the assumption thatχ,ξ,μ_(i),a_(i),α_(i) andβ_(i)(i=1,2)satisfy some suitable conditions.Subsequently,we also analyse the asymptotic behavior of solutions to the above system and show that·when a_(1)1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system exponentially converges to(0,α_(1)/β_(1),1,0)as t→∞;·when a1=1 andμ_(2)/ξ_(2) is sufficiently large,the global bounded classical solution(u,v,w,z)of this system polynomially converges to(0,α_(1)/β_(1),1,0)as t→∞.

关键词： Chemotaxis predator-prey boundedness stabilization

boundedness OF A CHEMOTAXIS-CONVECTION MODEL DESCRIBING TUMOR-INDUCED ANGIOGENESIS

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Acta Mathematica Scientia 2023年第1期43卷 156-168页

作者：金海洋徐凯滢 School of Mathematics South China University of TechnologyGuangzhou510640China

This paper is concerned with the parabolic-parabolic-elliptic system■in a bounded domainΩ?Rnwith a smooth boundary,where the parametersχ,ζ1,ζ2are positive constants and m≥1.Based on the coupled energy estimates,... 详细信息

关键词： boundedness convection chemotaxis tumor invasion

boundedness and convergence of perturbed corrections for helium-like ions in ground states

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Chinese Physics B 2008年第5期17卷 1720-1728页

作者：赵云辉海文华赵乘麟罗小兵 Department of Physics Hunan Normal University Department of Physics Shaoyang University Institute of Physics Chinese Academy of Sciences

Applying the improved Rayleigh SchrSdinger perturbation theory based on an integral equation to helium-like ions in ground states and treating electron correlations as perturbations, we obtain the second-order corrections to wavefunctions consisting of a few terms and the third-order corrections to energicity. It is demonstrated that the corrected wavefunctions are bounded and quadratically integrable, and the corresponding perturbation series is convergent. The results clear off the previous distrust for the convergence in the quantum perturbation theory and show a reciprocal development on the quantum perturbation problem of the ground state helium-like systems.

关键词： helium-like ion perturbation correction boundedness convergence

Blow-Up and boundedness in Quasilinear Parabolic-Elliptic Chemotaxis System with Nonlinear Signal Production

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偏微分方程:英文版 2023年第3期36卷 262-285页

作者： CAO Ruxi LI Zhongping College of Mathematics and Information China West Normal UniversityNanchong 637009China.

In this paper,we consider the quasilinear chemotaxis system of parabolicelliptic type■.under homogeneous Neumann boundary conditions in a smooth bounded domain■n≥1.The nonlinear diffusivity D(ζ)and chemosensitivity f(ζ)as well as nonlinear signal production g(ζ)are supposed to extend the prototypes■We proved that if m+k+l>1+2/n,then there exists nonnegative radially symmetric initial data uo such that the corresponding solutions blow up in finite time.However,the system admits a global bounded classical solution for arbitrary initial datum when m+k+l<1+2/n.

关键词： Chemotaxis nonlinear diffusion blow-up boundedness nonlinear signal production

boundedness AND ASYMPTOTIC STABILITY OFMULTISTEP METHODS FOR GENERALIZED PANTOGRAPH EQUATIONS

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Journal of Computational Mathematics 2004年第3期22卷 447-456页

作者： Cheng-jianZhang GengSun DepartmentofMathematics HuazhongUniversityofScienceandTechnologyWuhan430074China InstituteofMathematicsandSystemsScience ChineseAcademyofScienceBeijing100080China

In this paper, we deal with the boundedness and the asymptotic stability of linear and one-leg multistep methods for generalized pantograph equations of neutral type, which arise from some fields of engineering. Some ... 详细信息

关键词： boundedness Asymptotic stability Multistep methods Generalized pantograph equations