an:01682525
Zbl 0982.60055
Manthey, Ralf
The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space
EN
Math. Bohem. 126, No. 1, 15-39 (2001).
00081879
2001
j
60H15 35R60
Cauchy problem; nuclear and cylindrical noise; existence and uniqueness of the solution; spatial growth; ultimate boundedness; asymptotic mean square stability
Summary: The Cauchy problem for a stochastic partial differential equation with a spatial correlated Gaussian noise is considered. The ``drift'' is continuous, one-sided linearily bounded and of at most polynomial growth while the ``diffusion'' is globally Lipschitz continuous. Statements on existence and uniqueness of solutions, their pathwise spatial growth and on their ultimate boundedness as well as on asymptotical exponential stability in mean square in a certain Hilbert space of weighted functions are proved.