In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups...In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.展开更多
The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical s...The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed.展开更多
We consider a class of free boundary problems with Neumann boundary conditions.We would like to give certain results with regularity of solutions(mainly the local interior and boundary Lipschitz continuity).We will al...We consider a class of free boundary problems with Neumann boundary conditions.We would like to give certain results with regularity of solutions(mainly the local interior and boundary Lipschitz continuity).We will also show an explicit form of solution under well-specified conditions.展开更多
We analyze the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where additive noise occurs in the Neumann boundary condition. The convergence is established for general filtr...We analyze the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where additive noise occurs in the Neumann boundary condition. The convergence is established for general filtration, and the convergence rate O(τ1/4-?+ h1/2-?) is derived for the natural filtration of the Q-Wiener process.展开更多
An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;usi...An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.展开更多
Various optimal boundary control problems for linear infinite order distributed hyperbolic systems involving constant time lags are considered. Constraints on controls are imposed. Necessary and sufficient optimality ...Various optimal boundary control problems for linear infinite order distributed hyperbolic systems involving constant time lags are considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.展开更多
基金supported by the National Natural Science Foundation of China(No.11121101)the National Basic Research Program of China(No.2013CB834100)
文摘In this paper, for a coupled system of wave equations with iNeumann boundary controls, the exact boundary synchronization is taken into consideration. Results are then extended to the case of synchronization by groups. Moreover, the determination of the state of synchronization by groups is discussed with details for the synchronization and for the synchronization by 3-groups, respectively.
文摘The present paper focuses on the wave radiation by an oscillating body with six degrees of freedom by using the DtN artifi-cial boundary condition.The artificial boundary is usually selected as a circle or spherical surface to solve various types of fields,such as sound waves or electromagnetic waves,provided that the considered domain is infinite or unbounded in all directions.However,the substantial wave motion is considered in water of finite depth,that is,the fluid domain is bounded vertically but unbounded horizon-tally.Thus,the DtN boundary condition is given on an artificial cylindrical surface,which divides the water domain into an interior and exterior region.The boundary integral equation is adopted to implement the present model.In the case of a floating cylinder,the results of hydrodynamic coefficients of a chamfer box are discussed.
文摘We consider a class of free boundary problems with Neumann boundary conditions.We would like to give certain results with regularity of solutions(mainly the local interior and boundary Lipschitz continuity).We will also show an explicit form of solution under well-specified conditions.
基金supported by National Natural Science Foundation of China (Grant No.11901410)the Fundamental Research Funds for the Central Universities in China (Grant No. 2020SCU12063)。
文摘We analyze the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where additive noise occurs in the Neumann boundary condition. The convergence is established for general filtration, and the convergence rate O(τ1/4-?+ h1/2-?) is derived for the natural filtration of the Q-Wiener process.
文摘An innovative, extremely fast and accurate method is presented for Neumann-Dirichlet and Dirichlet-Neumann boundary problems for the Poisson equation, and the diffusion and wave equation in quasi-stationary regime;using the finite difference method, in one dimensional case. Two novels matrices are determined allowing a direct and exact formulation of the solution of the Poisson equation. Verification is also done considering an interesting potential problem and the sensibility is determined. This new method has an algorithm complexity of O(N), its truncation error goes like O(h2), and it is more precise and faster than the Thomas algorithm.
文摘Various optimal boundary control problems for linear infinite order distributed hyperbolic systems involving constant time lags are considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.
