带阻尼的随机波动方程的解的长时间行为（英文）
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摘要
主要考虑带阻尼的随机波动方程的解的长时间行为.在某些特定的条件下,证明了随机波动方程的解几乎处处指数稳定.最后给出了两个例子说明结果.
The long time behavior of the solution to a stochastic wave equation with damping is considered. Under some appropriate conditions, the exponential stability of the solutions holds almost surely.Finally two examples to illustrate the results are given.
The long time behavior of the solution to a stochastic wave equation with damping is considered. Under some appropriate conditions, the exponential stability of the solutions holds almost surely.Finally two examples to illustrate the results are given.
引文
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2 Chow P.Stochastic wave equation with polynimial nonlinearity[J].Ann Appl Probab,2002,12:361-381.
3 Chow P.Asymptotics of solutions to semilinear stochastic wave equations[J].Ann Appl Probab,2006,16:757-789.
4 Bo L,Tang D,Wang Y.Explosive solutions of stochastic wave equations with damping on Rd[J].J Differ Equ,2008,244:170-187.
5 Lv Y,Wang W.Limiting dynamics for stochastic wave euqtions[J].J Differential Equations,2008,244:1-23.
6 Liu K.Large time behaviour for a class of turbulence models-stochastic Burgers equations[J].J Phys A:Math Gen,1997,30:3 991-4 004.
7 Adams R.Sobolev Spaces[M].New York:Academic Press,1992.
8 Temam R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].2nd ed.New York:SpringerVerlag,1997.
9 Zeidler E.Nonlinear Functional Analysis and Its Applications[M].New York:Springer-Verlag,1990.
10 James A.On a inequality of Gronwall[J].J Inequalities in Pure and Appl Math,2001,2(1):1-6.
11 Da Prato G,Zabczyk J.Stochastic equations in infinite dimensions[M].Cambridge:Cambridge Univ Press,1992.
12 Mao X.Exponential Stability of Stochastic Differential Equations[M].New York:[s.n.],1994.