.png){kind=icon}
.png){kind=icon}
Return
Limiting Dynamics of BBM Equations with Nonlinear Colored Noise and Time-Delay on Unbounded Channel
.png){kind=icon}
PRE
AI
Z
C
DOI：10.1007/s00245-026-10413-3.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The aim of this paper is to establish the limiting behavior of random attractors for non-autonomous Benjamin-Bona-Mahony equations with nonlinear colored noise and time-delay defined on unbounded channels. A suitable condition to control the time-delay term is given and then several necessary uniform estimates on the solutions of the problem are established. The pullback asymptotical compactness of the non-autonomous cocycle associated with non-autonomous BBM equation with nonlinear colored noise and time-delay in C([-rho,0],H01(O))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C([-\rho ,0],H_0<^>1(\mathcal {O}))$$\end{document} is proved by virtue of the arguments of Arzela-Ascoli theorem, spectral decomposition as well as uniform tail-estimates in order to surmount several difficulties caused by the lack of compact Sobolev embeddings on unbounded domains and weak dissipative structure of the equation. Then the existence of tempered pullback random attractors of the equation is established in C([-rho,0],H01(O))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C([-\rho ,0],H_0<^>1(\mathcal {O}))$$\end{document} for nonlinear growth diffusion term as well as Lipschitz time-delay term. At last, the upper semi-continuity of two random attractors is investigated by utilizing the strategy of showing that the solution of BBM equation with time-delay convergent to the solution of non-delay BBM equation as the time delay approaches zero. This work extended our previous work [8, Mathematische Annalen, 2023] to non-autonomous BBM equation with time-delay and further considered the limiting behavior of random attractors.
Keywords:
Benjamin-Bona-Mahony equation with time-delay
Pullback random attractors
Nonlinear colored noise
Upper semi-continuity
Journal
A
IF:
1.7
Papers:
106
Citations:
0
Organization
Cited Papers