To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations a...To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.展开更多
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point ...In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.展开更多
The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so t...The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.展开更多
In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the probl...In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.展开更多
In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component bei...In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory展开更多
This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local so...This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem.展开更多
Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly pertur...Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.展开更多
In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a ...In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.展开更多
We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0...We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0）=m-2∑i=1biu]（ζi）,u（1）=m-2∑i=1aiu（ζi）.We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.展开更多
基金supported by the National Natural Science Foundation of China(Nos.61174221 and 61402039)
文摘To solve the receding horizon control （RHC） problem in an online manner, a novel numerical method called the indirect Radau pseudospectral method （IRPM） is proposed in this paper. Based on calculus of variations and the first-order necessary optimality condition, the RHC problem for linear time-varying （LTV） system is transformed into the two-point boundary value problem （TPBVP）. The Radau pseudospectral approximation is employed to discretize the TPBVP into well-posed linear algebraic equations. The resulting linear algebraic equations are solved via a matrix partitioning approach afterwards to obtain the optimal feedback control law. For the nonlinear system, the linearization method or the quasi linearization method is employed to approximate the RHC problem with successive linear approximations. Subsequently, each linear problem is solved via the similar method which is used to solve the RHC problem for LTV system. Simulation results of three examples show that the IRPM is of high accuracy and of high compu- tation efficiency to solve the RHC problem and the stability of closed-loop systems is guaranteed.
基金supported by the National Nature Science Foundation of China (10671167)
文摘In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type.
基金Supported by the National Natural Science Foundation of China (10161009)
文摘The Riemann boundary value problem with square roots in class h0 when the jumping curve is an open arc in the complex plane is considered. It is solved by reducing it to a classical Riemann boundary value problem so that its solutions are obtained in closed form. In certain cases, some auxiliary function ω（z）is introduced. With different choices of ω（z）＇s, some interesting examples are illustrated.
基金A Project Supported by Scientific Research Fund of Hunan Provincial Education Department (10C1056)Scientific Research Found of Huaihua University (HHUY2011-01)
文摘In this paper the authors consider the existence and uniqueness of the solution to the initial boundary value problem for a class of modified Zakharov equations, prove the global existence of the solution to the problem by a priori integral estimates and Galerkin method.
文摘In this article, we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials, one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary, while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory
基金Supported by the National Natural Science Foundation of China（10671182） Supported by the Excellent Youth Teachers Foundation of High College of Henan Province（2006110016）
文摘This paper gives the suffcient conditions of blow-up of the solution of a nonlinear hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local solution of the problem.
基金Project supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘Based on the precise integration method （PIM）, a coupling technique of the high order multiplication perturbation method （HOMPM） and the reduction method is proposed to solve variable coefficient singularly perturbed two-point boundary value prob lems （TPBVPs） with one boundary layer. First, the inhomogeneous ordinary differential equations （ODEs） are transformed into the homogeneous ODEs by variable coefficient dimensional expansion. Then, the whole interval is divided evenly, and the transfer ma trix in each sub-interval is worked out through the HOMPM. Finally, a group of algebraic equations are given based on the relationship between the neighboring sub-intervals, which are solved by the reduction method. Numerical results show that the present method is highly efficient.
基金Acknowledgments The author is supported by Tianyuan Foundation （No. 11026093） and the National Natural Science Foundation of China （Nos. 11101162, 11071086）.
文摘In this paper, we study the inviscid limit problem for the scalar viscous conservation laws on half plane. We prove that if the solution of the corresponding inviscid equation on half plane is piecewise smooth with a single shock satisfying the entropy condition, then there exist solutions to the viscous conservation laws which converge to the inviscid solution away from the shock discontinuity and the boundary at a rate of ε1 as the viscosity ε tends to zero.
基金Supported by the "Qing-Lan" Project of Jiangsu Education Committeethe Natural Science Foundation of Jiangsu Education Committee (Grant No. 02KJD460011)
文摘We consider the second-order differential equationu＂（t） ＋ q（t）f（t,u（t）,u＇（t）） =0, 0 〈 t 〈 1,subject to three-point boundry conditionu（0）=0, u（1） = aou（ζ0）,or to m-point boundary condition u＇（0）=m-2∑i=1biu]（ζi）,u（1）=m-2∑i=1aiu（ζi）.We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.
