Asymptotic solutions of a nonlinear stochastic beam equation

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.