This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We p...In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.展开更多
This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution un...This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.展开更多
In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="&q...In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).展开更多
This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect.We consider this problem in a bounded domainΩ■R^(3) under zero-flux boundary condition,and it is shown that the vol...This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect.We consider this problem in a bounded domainΩ■R^(3) under zero-flux boundary condition,and it is shown that the volume filling effect will prevent overcrowding behavior,and no blow up phenomenon happen.In fact,we show that for any initial datum,the problem admits a unique global-in-time classical solution,which is bounded uniformly.Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0≤u_(0)(x)≤1 withρ(x,t)≡1.However,when the maximum size of the aggregate is not a constant but rather a functionρ(x,t),ensuring the boundedness of the solutions becomes significantly challenging.This introduces a fundamental difficulty into the analysis.展开更多
In this paper,an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities.The considered system has no precise priori kno...In this paper,an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities.The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity.Firstly,a dynamic gain is introduced to deal with the unknown growth rate,and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse.Then,by virtue of hyperbolic functions and sign functions,a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system.Moreover,the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy.Finally,two simulation examples are given to verify the effectiveness of the control scheme.展开更多
This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic...This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.展开更多
A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and...A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.展开更多
This paper deals with a predator-prey model with indirect prey-taxis and predator-taxis{u_(t)=■·(D_(1)(u)■u)-χ■·(S_(1)(u)■z)+u(αv-a_(1)-b_(1)u),x∈Ω,t>0,u_(t)=■·(D_(2)(v)■v)-ε■·(S_(1)...This paper deals with a predator-prey model with indirect prey-taxis and predator-taxis{u_(t)=■·(D_(1)(u)■u)-χ■·(S_(1)(u)■z)+u(αv-a_(1)-b_(1)u),x∈Ω,t>0,u_(t)=■·(D_(2)(v)■v)-ε■·(S_(1)(v)■w)+v(a_(2)-b_(2)v),x∈Ω,t>0,0=△ω+βu-γw,x∈Ω,t>0,0=△z+δv-ρz,x∈Ω,t>0,under homogeneous Neumann boundary conditions in a smoothly bounded domainΩblong to R^(n)(n≥1),where the parametersχ,ε,α,β,γ,δ,ρ,a_(1),a_(2),b_(1),b_(2)are positive,D_(1)(u)and D_(2)(v)are nonlinear diffusion functions,Si(u)and S2(v)are nonlinear sensitivity functions.First,under certain suitable conditions for D,and S,with i=1,2,the system admits a unique globally bounded classical solution,provided that b_(1)≥4αand b_(2)>0.Additionally,by constructing appropriate Lyapunov functionals,we investigate the asymptotic stability of the globally bounded solutions and provide the exact convergence rates based on the different parameter choices.展开更多
基金Supported the National Natural Science Foundation of China（10471080） Supported by the Natural Science Foundation of Henan Province（2004110008）
文摘This paper is devoted to the mixed initial-boundary value problem for the semiconductor equations. Using Stampacchia recurrence method, we prove that the solutions areglobally bounded and positive.
基金supported by the Jilin Scientific and Technological Development Program(20210101466JC).
文摘In this paper,we consider the following spatial Solow-Swan model with density-dependent motion■whereσ>0,α∈(0,1)andΩ⊂ℝn(n≥1)is a bounded domain with smooth boundary andϕ∈C3([0,∞)),ϕ(s)>0 for all s≥0.We prove that if■then there exists a unique time-globally classical solution(u,v)for all n≥1,such a solution is bounded and satisfies u≥0,v>0.Moreover,we show that the above solution will convergence to the steady state(1,1)exponentially in L^(∞)as t→∞.
基金Supported by the National Natural Science Foundation of China(11301419)the Research and innovation Team of China West Normal University(CXTD2020-5)。
文摘This paper deals with a chemotaxis-haptotaxis system with ECM-dependent sensitivity under the Neumann boundary conditions in a smooth bounded domain.It is shown that the system possesses a globally bounded solution under some conditions.
基金Supported by the NSF of Jiangxi Province, the NSFC (10225105, 10671023) and a CAEP grant
文摘In this article, the globally bounded in-time pointwise estimate of solutions to the simplified Keller-Segel system modelling chemotaxis are derived. Moreover, a local existence theorem is obtained.
文摘In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity <img src="Edit_4b941130-fc1e-4c9b-9626-4fd5a1f03836.bmp" alt="" />(0.1)<br /> is considered in a bounded domain with smooth boundary, Ω ⊂R<sup>n</sup> (n ≥ 1), where d<sub>1</sub> > 0, d<sub>2</sub> > 0 with parameter χ ∈ R. When d<sub>1</sub> = d<sub>2</sub> + χ, satisfying for all initial data 0 ≤ n<sub>0</sub> ∈ C<sup>0</sup><img src="Edit_4898c7a9-f047-4856-b9ad-8d42ecf262a2.bmp" alt="" /> and 0 < v<sub>0</sub>∈ W<sup>1,∞</sup> (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).
基金supported by National Natural Science Foundation of China(12271186,11871230).
文摘This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect.We consider this problem in a bounded domainΩ■R^(3) under zero-flux boundary condition,and it is shown that the volume filling effect will prevent overcrowding behavior,and no blow up phenomenon happen.In fact,we show that for any initial datum,the problem admits a unique global-in-time classical solution,which is bounded uniformly.Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0≤u_(0)(x)≤1 withρ(x,t)≡1.However,when the maximum size of the aggregate is not a constant but rather a functionρ(x,t),ensuring the boundedness of the solutions becomes significantly challenging.This introduces a fundamental difficulty into the analysis.
基金supported by the National Natural Science Foundation of China(Nos.61973189,62073190)the Research Fund for the Taishan Scholar Project of Shandong Province of China(No.ts20190905)the Natural Science Foundation of Shandong Province of China(No.ZR2020ZD25).
文摘In this paper,an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities.The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity.Firstly,a dynamic gain is introduced to deal with the unknown growth rate,and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse.Then,by virtue of hyperbolic functions and sign functions,a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system.Moreover,the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy.Finally,two simulation examples are given to verify the effectiveness of the control scheme.
基金supported by the National Natural Science Foundation of China(61304020)
文摘This paper is concerned with the global boundedness problem for a class of stochastic nonlinear systems with matched conditions. The uncertainties in the systems are due to parameter variations and external stochastic disturbance. Only the matched conditions and the possible bound of the uncertainties are demanded. Based on the stochastic Lyapunov stability theory, an explicit controller is constructed in the gradient direction, which renders responses of the closed-loop systems be globally bounded in probability. When the systems degrade to linear systems, the controller becomes linear. Illustrative examples are given to show the effectiveness of the proposed method.
文摘A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.
基金supported by the National Natural Science Foundation of China(Grant Nos.11601053,12271064)the Science and Technology Research Project of Chongqing Municipal Education Commission(Grant No.KJZD-K202200602)+1 种基金the Natural Science Foundation of Chongqing(Grant No.CSTB2023NSCQ-MSX0099)the Hong Kong Scholars Program(Grant Nos.XJ2021042,2021-005)and the Young Hundred Talents Program of CQUPT in 2022-2024.
文摘This paper deals with a predator-prey model with indirect prey-taxis and predator-taxis{u_(t)=■·(D_(1)(u)■u)-χ■·(S_(1)(u)■z)+u(αv-a_(1)-b_(1)u),x∈Ω,t>0,u_(t)=■·(D_(2)(v)■v)-ε■·(S_(1)(v)■w)+v(a_(2)-b_(2)v),x∈Ω,t>0,0=△ω+βu-γw,x∈Ω,t>0,0=△z+δv-ρz,x∈Ω,t>0,under homogeneous Neumann boundary conditions in a smoothly bounded domainΩblong to R^(n)(n≥1),where the parametersχ,ε,α,β,γ,δ,ρ,a_(1),a_(2),b_(1),b_(2)are positive,D_(1)(u)and D_(2)(v)are nonlinear diffusion functions,Si(u)and S2(v)are nonlinear sensitivity functions.First,under certain suitable conditions for D,and S,with i=1,2,the system admits a unique globally bounded classical solution,provided that b_(1)≥4αand b_(2)>0.Additionally,by constructing appropriate Lyapunov functionals,we investigate the asymptotic stability of the globally bounded solutions and provide the exact convergence rates based on the different parameter choices.
