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July  2006, 6(4): 735-749. doi: 10.3934/dcdsb.2006.6.735

Asymptotic solutions of a nonlinear stochastic beam equation

Pao-Liu Chow 1,

1. 

Department of Mathematics, Wayne State University, Detroit, MI 48202, United States

Received  February 2005 Revised  October 2005 Published  April 2006

Large-time asymptotic properties of solutions to a semilinear stochastic beam equation with damping in a bounded domain is considered. First an energy inequality and the exponential bound for a linear stochastic beam equation is established. Under appropriate conditions, the existence and uniqueness theorem for the nonlinear stochastic beam equation is proved. Next the main results on the boundedness of global solutions and the exponential stability of an equilibrium solution, in the mean-square sense, are given. Two examples are presented to illustrate some applications of the theorems.
Keywords: nonlinear partial integro-differential equation, bounded solutions, Stochastic beam equation, exponential stability..
Mathematics Subject Classification: Primary: 60H05, 60H15; Secondary: 60H0.
Citation: Pao-Liu Chow. Asymptotic solutions of a nonlinear stochastic beam equation. Discrete and Continuous Dynamical Systems - B, 2006, 6 (4) : 735-749. doi: 10.3934/dcdsb.2006.6.735
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