By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u ...By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u 〉 0, x ∈ Ω, u｜δΩ =＋∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞）, g（0） = g＇（0） = 0, and there exists p 〉 1, such that lim g（sξ）/g（s）=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α（Ω） is non-negative non-trivial in D which may be singular on the boundary.展开更多
In this paper,a new stochastic analysis tool on semi-global stability is constructed,for nonlinear systems disturbed by stochastic processes with strongly bounded in probability.The definition of semi-global noise to ...In this paper,a new stochastic analysis tool on semi-global stability is constructed,for nonlinear systems disturbed by stochastic processes with strongly bounded in probability.The definition of semi-global noise to state practical stability in probability and its Lyapunov criterion for random systems are presented.As a major application of stability,the semi-global practical tracking of random nonlinear systems based on dynamic surface control technique is considered.The trajectory tracking of manipulator robot driven by direct current motors is carried out in simulation to illustrate the effectiveness and feasibility of the control scheme.展开更多
This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special inte...This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.展开更多
In this paper, we first study the existence of transition fronts （generalized traveling fronts） for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution a...In this paper, we first study the existence of transition fronts （generalized traveling fronts） for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts.展开更多
The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper.Since the modes mismatch problem often exists in the Markovian switching system,the authors design a mo...The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper.Since the modes mismatch problem often exists in the Markovian switching system,the authors design a modes asynchronous controller with an internal model form,which can not only deal with external disturbance,but also reduce the influence of stochastic noise on the system,such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters.Meanwhile,a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.展开更多
基金supported by the National Natural Science Foundation of China (10671169)
文摘By Karamata regular variation theory and constructing comparison functions, the author shows the existence and global optimal asymptotic behaviour of solutions for a semilinear elliptic problem Δu = k（x）g（u）, u 〉 0, x ∈ Ω, u｜δΩ =＋∞, where Ω is a bounded domain with smooth boundary in R^N; g ∈ C^1[0, ∞）, g（0） = g＇（0） = 0, and there exists p 〉 1, such that lim g（sξ）/g（s）=ξ^p, ↓Aξ 〉 0, and k ∈ Cloc^α（Ω） is non-negative non-trivial in D which may be singular on the boundary.
基金supported by the National Natural Science Foundations of China under Grant No.62073275。
文摘In this paper,a new stochastic analysis tool on semi-global stability is constructed,for nonlinear systems disturbed by stochastic processes with strongly bounded in probability.The definition of semi-global noise to state practical stability in probability and its Lyapunov criterion for random systems are presented.As a major application of stability,the semi-global practical tracking of random nonlinear systems based on dynamic surface control technique is considered.The trajectory tracking of manipulator robot driven by direct current motors is carried out in simulation to illustrate the effectiveness and feasibility of the control scheme.
基金Supported by the National Natural Science Foundation of China(11071172,11201402,11201266)Beijing Natural Science Foundation(1132003)+1 种基金Beijing Municipal Education Commission(KZ201310028030)Tianyuan Youth Foundations for Mathematics of NNSFC(11026098,11026150)
文摘This paper is concerned with the global existence and uniform boundedness of solutions for two classes of chemotaxis models in two or three dimensional spaces. Firstly, by using detailed energy estimates, special interpolation relation and uniform Gronwall inequality, we prove the global existence of uniformly bounded solutions for a class of chemotaztic systems with linear chemotactic-sensitivity terms and logistic reaction terms. Secondly, by applying detailed analytic semigroup estimates and special iteration techniques, we obtain the global existence of uniformly bounded solutions for a class of chemotactic systems with nonlinear chemotacticsensitivity terms, which extends the global existence results of [6] to other general cases.
基金Supported by NSF of China(Grant No.11031003)NSF of Shandong Province of China(Grant No.ZR2010AQ006)
文摘In this paper, we first study the existence of transition fronts （generalized traveling fronts） for reaction-diffusion equations with the spatially heterogeneous bistable nonlinearity. By constructing sub-solution and super-solution we then show that transition fronts are globally exponentially stable for the solutions of the Cauchy problem. Furthermore, we prove that transition fronts are unique up to translation in time by using the monotonicity in time and the exponential decay of such transition fronts.
基金This work was partially supported by the National Natural Science Foundation of China under Grant No.U1966202.
文摘The output regulation control problem for the Markovian jump systems with colored-noise is proposed in this paper.Since the modes mismatch problem often exists in the Markovian switching system,the authors design a modes asynchronous controller with an internal model form,which can not only deal with external disturbance,but also reduce the influence of stochastic noise on the system,such that the mean square of the regulation error can be made arbitrarily small by turning the designed parameters.Meanwhile,a criterion of the m-th moment noise-to-state exponential stability is presented for continuous-time Markovian jump systems under the asynchronous control.
