Pathwise stationary solutions of stochastic Burgers equations with $L^2[0,1]$-noise and stochastic Burgers integral equations on infinite horizon
| dc.creator | Liu, Yong | |
| dc.creator | Zhao, Huaizhong | |
| dc.date | 2006-09-13 | |
| dc.date.accessioned | 2026-07-07T07:24:46Z | |
| dc.date.available | 2026-07-07T07:24:46Z | |
| dc.description | In this paper, we show the existence and uniqueness of the stationary solution $u(t,ω)$ and stationary point $Y(ω)$ of the differentiable random dynamical system $U:R\times L^2[0,1]\times Ω\to L^2[0,1]$ generated by the stochastic Burgers equation with $L^2[0,1]$-noise and large viscosity, especially, $u(t,ω)=U(t,Y(ω),ω)=Y(θ(t,ω))$, and $Y(ω) \in H^1[0,1]$ is the unique solution of the following equation in $L^2[0,1]$ $$ Y(ω)={1/2}\int_{-\infty}^0T_ν(-s)\frac{\partial (Y(θ(s,ω))^2}{\partial x}ds +\int_{-\infty}^0T_ν(-s)dW_s(ω), $$ where $θ$ is the group of $P$-preserving ergodic transformation on the canonical probability pace $(Ω, {\cal F}, P)$ such that $θ(t,ω)(s)=W(t+s)-W(t)$. | |
| dc.identifier | https://arxiv.org/abs/math/0609344 | |
| dc.identifier | http://arxiv.org/abs/math/0609344 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116492 | |
| dc.subject | Probability | |
| dc.subject | Analysis of PDEs | |
| dc.title | Pathwise stationary solutions of stochastic Burgers equations with $L^2[0,1]$-noise and stochastic Burgers integral equations on infinite horizon | |
| dc.type | text |