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刘斌, Hanwen Ning and Bin Liu
Applicable Analysis, Vol. 88, No. 4, April 2009, 563–577,-0001,():
-1年11月30日
In this article, we consider dynamic behaviours of a class of non-linear delay stochastic evolution equations. Local existence and uniqueness of the solutions are obtained with the aid of proper iterative scheme and moment estimations. We also propose a continuation result and our results generalize the known results.
stochastic evolution equations, local existence, uniqueness,
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【期刊论文】ON EXPONENTIAL STABILITY FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS
刘斌, Guosheng Yu and Bin Liu
Stochastics and Dynamics, Vol. 9, No. 1 (2009) 121–134,-0001,():
-1年11月30日
This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, one example is also given to illustrate our results.
Stochastic delay partial differential equations, energy solutions, energy equation
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刘斌, Huaiqiang Yu and Bin Liu
J. Math. Anal. Appl. 395 (2012) 654–672,-0001,():
-1年11月30日
We study the boundary control problems for stochastic parabolic equations with Neumann boundary conditions. Imposing super-parabolic conditions, we establish the existence and uniqueness of the solution of state and adjoint equations with non-homogeneous boundary conditions by the Galerkin approximations method. We also find that, in this case, the adjoint equation (BSPDE) has two boundary conditions (one is non-homogeneous, the other is homogeneous). By these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method.
Stochastic partial differential equations, Boundary control, Necessary conditions
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【期刊论文】Existence Results for Impulsive Neutral Stochastic Evolution Inclusions in Hilbert Space
刘斌, Hanwen Ning and Bin Liu
Acta Mathematica Sinica, 2011, 27(7), 1405–1418,-0001,():
-1年11月30日
This paper is concerned with the existence of mild solutions of a class of impulsive neutral stochastic evolution inclusions in Hilbert space in the case where the right hand side is convex or nonconvex-valued. The results are obtained by using two fixed point theorems for multivalued mappings and evolution system theory.
Impulsive,, mild solutions,, stochastic evolution inclusions,, convex,, nonconvex
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【期刊论文】A maximum principle for optimal control system with endpoint constraints
刘斌, Weifeng Wang and Bin Liu
Journal of Inequalities and Applications 2012, 2012,-0001,():
-1年11月30日
Pontryagin’s maximum principle for an optimal control system governed by an ordinary differential equation with endpoint constraints is proved under the assumption that the control domain has no linear structure. We also obtain the variational equation, adjoint equation and Hamilton system for our problem.
Pontryagin’s maximum principle, optimal control, Hamilton system,
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