河北师范大学学报——哲学社会科学版

期刊信息

刊名：河北师范大学学报（哲学社会科学版）Journal of Hebei Normal University (Philosophy and Social Sciences Edition)
主办：河北师范大学
ISSN： 1000-5587
CN： 13-1029/C
该刊被以下数据库收录：
AMI综合评价（A刊）核心期刊
RCCSE中国核心学术期刊
中国期刊方阵入选期刊
全国百强社会科学学报
中国人民大学“复印报刊资料”重要转载来源期刊

友情链接

非自治半线性退化随机抛物方程的动力学行为

收稿日期： 2016-12-20

作者单位： 河海大学理学院, 江苏南京 211100
起止页码： 192 - 199页

Dynamic Behavior for Non-autonomous Stochastic Semi-linear Degenerate Parabolic Equations

DU Ziming, JIANG Yong, LI Xiaojun

PDF
下载
HTML

摘要/Abstract

摘要：

研究了半线性退化随机抛物方程随机吸引子的存在性，其中非线性项具有任意的增长指数，随机部分是依赖于空间分布和时间的白噪声.通过对变换系统解的估计与正则估计，得到渐近紧的D-拉回吸收集的存在性，从而得到随机吸引子的存在性.

Abstract：

In this paper, we study the existence of random attractor for stochastic semi-linear degenerate parabolic equations, where the nonlinearity term satisfies the arbitrary order, and the stochastic term is white noise depending on spatial distribution and time. By estimate and regular estimate of solutions of transformed system, we obtain the existence of asymptotically compact D-pullback absorbing set, and thus the existence of random attractor.

关键词

关键词： 非自治系统 ; 随机系统 ; 抛物方程 ; 随机吸引子 ;

Key words： non-autonomous system ; stochastic system ; parabolic equations ; random attractor ;

参考文献 12

[ 1 ] ANH C T,THUY L T,Notes on Global Attractors for a Class of Semilinear Degenerate Parabolic Equations[J].J Nonlinear Evol Equ Appl,2012,4:41-56.doi:10.1007/s00028-013-0196-0
[ 2 ] ANH C T,BINH N D,THUY L T.On the Global Attractors for a Class of Semilinear Degenerate Parabolic Equations[J].Ann Pol Math,2010,98:71-89.
[ 3 ] ANH C T,HUANG P Q,Global Existence and Long-time Behavior of Solutions to a Class of Degenerate Parabolic Equations[J].Ann Pol Math,2008,93:217-230.doi:10.4064/ap93-3-3
[ 4 ] ANH C T,BAO T Q,Pullback Attractors for a Non-autonomous Semi-linear Degenerate Parabolic Equation[J].Glasgow Math J,2010,52:537-554.doi:10.1017/S0017089510000418
[ 5 ] ANH C T,BAO T Q,THANH N V.Regularity of Random Attractors for Stochastic Semi-linear Degenerate Parabolic Equations[J].Electron J Differential Equation,2012,2207:1-22.
[ 6 ] ANH C T,BAO T Q,THUY L T.Regularity and Fractal Dimension of Pullback Attractors for a Non-autonomous Semilinear Degenerate Parabolic Equation[J].Glasgow Math J,2013,55:431-448.doi:10.1017/S0017089512000663
[ 7 ] YANG M H,KLOEDEN P E.Random Attractors for Stochastic Semi-linear Degenerate Parabolic Equations[J].Nonlinear Anal:Real World Appl,2011,12:2811-2821.doi:10.1016/j.nonrwa.2011.04.007.
[ 8 ] YIN J Y,LI Y R,ZHAO H J.Random Attractors for Stochastic Semi-linear Degenerate Parabolic Equations with Additive Noise in L_q[J].Appl Math Comput,2013,225:526-540.doi:10.1016/j.amc.2013.09.051
[ 9 ] ZHAO W Q.Regularity of Random Attractors for a Degenerate Parabolic Equations Driven by Additive Noises[J].Appl Math Comput,2014,239:358-374.doi:10.1016/S0252-9602(16)3009-1
[ 10 ] BATES P W,LU K N,WANG B X.Random Attractors for Stochastic Reaction-diffusion Equations on Unbounded Domains[J].J Differential Equation,2009,246:845-869.doi:10.1016/j.jde.2008.05.017
[ 11 ] CRAUEL H,FLANDOLI F.Attractors for Random Dynamical Systems[J].Probab Theory Related Fields,1994,100:365-393.doi:10.1007/BF 01193705
[ 12 ] WANG B X.Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-com-pact Random Dynamical Systems[J].J Differential Equation,2012,253:1544-1583.doi:10.1016/j.jde.2012.05.015