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

Mathematica Bohemica (2001)

- Volume: 126, Issue: 1, page 15-39
- ISSN: 0862-7959

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topManthey, Ralf. "The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space." Mathematica Bohemica 126.1 (2001): 15-39. <http://eudml.org/doc/248845>.

@article{Manthey2001,

abstract = {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.},

author = {Manthey, Ralf},

journal = {Mathematica Bohemica},

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

language = {eng},

number = {1},

pages = {15-39},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {The long-time behaviour of the solutions to semilinear stochastic partial differential equations on the whole space},

url = {http://eudml.org/doc/248845},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Manthey, Ralf

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

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 1

SP - 15

EP - 39

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/248845

ER -

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