This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ...This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.展开更多
This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),...This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.展开更多
This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t&g...This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t>0 w_(t)=-δw+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(n)(n≥1),where the parametersμ,δ>0 andγ>1,the functions D(u)and S(u)are supposed to be smooth fulfilling D(u)≥C_(D)(u+1)^(-a)and S(u)≤C_(S)u(u+1)^(β-1)for all u≥0 with C D,α,β∈R and.It is proved that the corresponding initial-boundary value problem possesses a global bounded classical solution ifα+2β<γ-1.Moreover,ifμis suitably large,the asymptotic behavior and convergence rates are also been considered.展开更多
In this paper,we study the asymptotic behavior of solutions to a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source{ut=■·(D(u)■u)-■·(S(u)■v)+b-μur,x∈Ω,t&...In this paper,we study the asymptotic behavior of solutions to a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source{ut=■·(D(u)■u)-■·(S(u)■v)+b-μur,x∈Ω,t>0,vt=Δv+a1v+b1w,x∈Ω,t>0,wt=Δw-a2w+b2u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(N)(N≥1),where b≥0,γ≥1,ai≥1,μ,bi>0(i=1,2,D,S∈C^(2)([0,∞))fulfilling D(S)≥a0(s+1)^(-a),0≤S(s)≤b0(s+1)^(β)for all s≥0,where a0,b0>0 and a,β≤R are constants.The pur purpose of this paper is to prove that if b≥0 andμ>0 sufficiently large,the globally bounded solution(u,v,w)with nonnegative initial data(u0,v0,w0)satisfies||u(·,t)-(b/μ)^(1/γ)L∞(Ω)+||V(·,t)+b1b2/a1a2(b/μ)^(1/γ)||L∞(Ω)+||w(·,t)+b2/a2(b/μ)^(1/γ)||L∞(Ω)→0ast→∞.展开更多
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≥...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).展开更多
In this paper, we focus on the qualitative analysis of a parabolic^lliptic attraction- repulsion chemotaxis model with logistic source. Applying a fixed point argument, LP- estimate technique and Moser＇s iteration, w...In this paper, we focus on the qualitative analysis of a parabolic^lliptic attraction- repulsion chemotaxis model with logistic source. Applying a fixed point argument, LP- estimate technique and Moser＇s iteration, we derive that the model admits a unique 1 global solution provided the initial cell mass satisfying ｜｜u0｜｜L1≤ X4/xaCGN-2＋1/σ＋1σ（σ ＋ 1）-1/σ-1｜Ω｜ for σ = 1. While for σ〉 1, there are no restrictions on the initial cell mass and the result still holds.展开更多
In this paper, we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source {ut=△uχ·(u/v■v)+ru-μu^(k),x∈Ω,t>0,O=△u-v+u,x∈Ω,t&...In this paper, we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source {ut=△uχ·(u/v■v)+ru-μu^(k),x∈Ω,t>0,O=△u-v+u,x∈Ω,t>0 in a smooth bounded domain ? ? R~n(n > 2) with the non-flux boundary, where χ, r, μ > 0,k ≥ 2. It is proved that the global bounded classical solution will exponentially converge to((r/μ)^(1/k-1),(r/μ)^(1/k-1)) as t →∞ if r is suitably large.展开更多
基金supported by the National Natural Science Foundation of China(12301251,12271232)the Natural Science Foundation of Shandong Province,China(ZR2021QA038)the Scientific Research Foundation of Linyi University,China(LYDX2020BS014)。
文摘This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.
基金This work is supported by the Youth Doctor Science and Technology Talent Training Project of Xinjiang Uygur Autonomous Region(2017Q087).
文摘This article considers the following higher-dimensional quasilinear parabolic-parabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions{ut=∇⋅(D(u)∇u)−∇⋅(S(u)∇v)+f(u),x∈Ω,t>0 vt=Δv+w−v,x∈Ω,t>0,wt=u−w,x∈Ω,t>0,in a bounded domainΩ⊂R^n(n≥2)with smooth boundary ∂Ω,where the diffusion coefficient D(u)and the chemotactic sensitivity function S(u)are supposed to satisfy D(u)≥M1(u+1)^−αand S(u)≤M2(u+1)^β,respectively,where M1,M2>0 and α,β∈R.Moreover,the logistic source f(u)is supposed to satisfy f(u)≤a−μu^γ with μ>0,γ≥1,and a≥0.Asα+2β<γ−1+2γ/n,we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.
基金Supported by the Science and Technology Research Project of Chongqing Education Commission(KJQN202000618)。
文摘This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t>0 w_(t)=-δw+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(n)(n≥1),where the parametersμ,δ>0 andγ>1,the functions D(u)and S(u)are supposed to be smooth fulfilling D(u)≥C_(D)(u+1)^(-a)and S(u)≤C_(S)u(u+1)^(β-1)for all u≥0 with C D,α,β∈R and.It is proved that the corresponding initial-boundary value problem possesses a global bounded classical solution ifα+2β<γ-1.Moreover,ifμis suitably large,the asymptotic behavior and convergence rates are also been considered.
基金The paper is supported by the National Science Foundation of China(11301419)the Meritocracy Research Funds of China West Normal University[17YC382].
文摘In this paper,we study the asymptotic behavior of solutions to a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source{ut=■·(D(u)■u)-■·(S(u)■v)+b-μur,x∈Ω,t>0,vt=Δv+a1v+b1w,x∈Ω,t>0,wt=Δw-a2w+b2u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(N)(N≥1),where b≥0,γ≥1,ai≥1,μ,bi>0(i=1,2,D,S∈C^(2)([0,∞))fulfilling D(S)≥a0(s+1)^(-a),0≤S(s)≤b0(s+1)^(β)for all s≥0,where a0,b0>0 and a,β≤R are constants.The pur purpose of this paper is to prove that if b≥0 andμ>0 sufficiently large,the globally bounded solution(u,v,w)with nonnegative initial data(u0,v0,w0)satisfies||u(·,t)-(b/μ)^(1/γ)L∞(Ω)+||V(·,t)+b1b2/a1a2(b/μ)^(1/γ)||L∞(Ω)+||w(·,t)+b2/a2(b/μ)^(1/γ)||L∞(Ω)→0ast→∞.
基金supported by the NSFC(12301260)the Hong Kong Scholars Program(XJ2023002,2023-078)+14 种基金the Double First-Class Construction-Talent Introduction of Southwest University(SWU-KR22037)the Chongqing Post-Doctoral Fund for Staying in Chongqing(2022)partially supported by the NSFC(12271064,11971082)the Chongqing Talent Support Program(cstc2022ycjh-bgzxm0169)the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX1051)the Fundamental Research Funds for the Central Universities(2020CDJQY-Z001,2019CDJCYJ001)the Key Laboratory of Nonlinear Analysis and its Applications(Chongqing University)Ministry of EducationChongqing Key Laboratory of Analytic Mathematics and Applicationssupported by the NSFC(12301261)the Scientific Research Starting Project of SWPU(2021QHZ016)the Sichuan Science and Technology Program(2023NSFSC1365)the Nanchong Municipal Government-Universities Scientific Cooperation Project(SXHZ045)supported by the China Scholarship Council(202206050060)the Graduate Research and Innovation Foundation of Chongqing(CYB22044)。
文摘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).
基金This work was supported by the National Natural Science Foundation of China （No. 61261044）.
文摘In this paper, we focus on the qualitative analysis of a parabolic^lliptic attraction- repulsion chemotaxis model with logistic source. Applying a fixed point argument, LP- estimate technique and Moser＇s iteration, we derive that the model admits a unique 1 global solution provided the initial cell mass satisfying ｜｜u0｜｜L1≤ X4/xaCGN-2＋1/σ＋1σ（σ ＋ 1）-1/σ-1｜Ω｜ for σ = 1. While for σ〉 1, there are no restrictions on the initial cell mass and the result still holds.
基金Supported by Innovation Team of China West Normal University (Grant No. CXTD2020-5)the Meritocracy Research Funds of China West Normal University (Grant No. 17YC372)。
文摘In this paper, we study the asymptotic behavior of solutions to the parabolic-elliptic chemotaxis system with singular sensitivity and logistic source {ut=△uχ·(u/v■v)+ru-μu^(k),x∈Ω,t>0,O=△u-v+u,x∈Ω,t>0 in a smooth bounded domain ? ? R~n(n > 2) with the non-flux boundary, where χ, r, μ > 0,k ≥ 2. It is proved that the global bounded classical solution will exponentially converge to((r/μ)^(1/k-1),(r/μ)^(1/k-1)) as t →∞ if r is suitably large.
