The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space

Title:

The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space

Creator:

Manthey, Ralf

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:09dcc077-e4d6-4b35-9629-80a9956eb11d
uuid:09dcc077-e4d6-4b35-9629-80a9956eb11d
doi:10.21136/MB.2001.133912

Subject:

nuclear and cylindrical noise, existence and uniqueness of the solution, spatial growth; ultimate boundedness, asymptotic mean square stability, and Cauchy problem

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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. In the paper 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

15-39

Source:

Mathematica bohemica | 2001 Volume:126 | Number:1

Harvested from:

CDK

Metadata only:

false