广西师范大学学报（自然科学版） ›› 2020, Vol. 38 ›› Issue (2): 134-143.doi: 10.16088/j.issn.1001-6600.2020.02.016

• CCIR2019 • 上一篇    下一篇

无界域上非自治随机反应扩散方程一致随机吸引子的存在性

张杰, 李晓军*   

  1. 河海大学理学院,江苏南京210098
  • 收稿日期:2018-12-11 发布日期:2020-04-02
  • 通讯作者: 李晓军(1970—),男,甘肃定西人,河海大学教授,博士。E-mail:lixjun05@hhu.edu.cn
  • 基金资助:
    国家自然科学基金(11571092)

Existence of Uniform Random Attractor for NonautonomousStochastic Reaction-diffusion Equations on Unbounded Domains

ZHANG Jie, LI Xiaojun*   

  1. School of Science, Hehai University, Nanjing Jiangsu 210098, China
  • Received:2018-12-11 Published:2020-04-02

PDF (PC)

424

摘要： 本文研究无界域上一类带有白噪声的非自治随机反应扩散方程一致吸引子的存在性。首先通过对解的一致估计, 证明了对应于原方程的随机动力系统拥有关于符号空间的一致拉回吸收集;其次, 通过渐近尾部估计得到解是一致拉回渐近紧性, 从而得到原系统一致随机吸引子的存在性。

关键词: 随机反应扩散方程, 一致吸引子, 无界域, 白噪声, 渐近紧性

Abstract: This paper studies the existence of uniform attractors for a class of nonautonomous stochastic reaction-diffusion equations with white noise on unbounded domains. Firstly, with uniform estimation of the solutions, it is proved that the stochastic dynamical system corresponding to the original equation has a uniformly with respect to symbol space pullback absorbing set. Secondly, by asymptotic tail estimation, it is proved that the solution is uniformly pullback and asymptotically compact. The existence of uniform random attractor of the original system is obtained.

Key words: tochasticreaction-diffusionequation, uniformattractor, unboundeddomain, whitenoise

中图分类号: 

  • O175.29
[1] BABIN A V, VISHIK M I. Attractors of evolution equations[M]. Burlington, MA:Elsevier, 1992.
[2] HALE J K. Asymptotic behaviour of dissipative systems[M].Providence,RI: MAA Press, 1988.
[3] TEMAM R. Infinite dimensional dynamical systems in mechanics and physics[M].New York, NY: Springer ,1997.
[4] FLANDOLI F, SCHMALFUSS B. Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise[J].Stochastics: An International Journal of Probability and Stochastic Processes,1996,59(1/2): 21-45.
[5] CRAUEL H, DEBUSSCHE A, FLANDOLI F. Random attractors[J].Journal of Dynamics & Differential Equations,1997,9(2): 307-341.
[6] CRAU E H, FLANDOLI F. Attractors for random dynamical systems[J].Probability Theory & Related Fields,1994,100(3): 365-393.
[7] WANG B X. Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamical systems[J].Journal of Differential Equations,2012,253(5): 1544-1583.
[8] WANG B X. Random attractors for non-automonous stochastic wave equations with multiplicative noise[J].Discrete & Continuous Dynamical Systems-A,2014,34: 269-300.
[9] CHEPYZHOV V V, VISHIK M I. Attractors for equations of mathematical physics[M]. Providence, RI: MAA Press, 2002.
[10]CUI H Y, LANGA J A. Uniform attractors for non-autonomous random dynamical systems[J].Journal of Differential Equations,2017,263(2): 1225-1268.
[11]SUN C Y, CAO D M, DUAN J Q. Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity[J]. Nonlinearity,2006,19: 2645-1268.
[12]CAO D M, SUN C Y, YANG M H. Dynamics for a stochastic reaction-diffusion equation with additive noise[J]. Journal of Differential Equations, 2015, 259(3): 838-872.
[13]BATES P W, LU K N, WANG B X. Random attractors for stochastic reaction-diffusion equations on unbounded domains[J].Journal of Differential Equations,2009,246: 845-869.
[14]WANG Z J, ZHOU F. Random attractor for non-autonomous stochastic strongly damped wave equation on unbounded damains[J].Journal of Applied Analysis and Computation,2015,5(3): 363-387.
[15]WANG B X. Random attractors for non-autonomous stochastic wave equations with multiplicative noise[J].Discrete & Continuous Dynamical Systems-A,2014,34(1): 269-300.
[16]WANG B X. Sufficient and necessary criteria for existence of pullback attractors for non-compact random dynamcial systems[J].Journal of Differential Equations,2012,253: 1544-1583.
[17]ARNOLD L. Random dynamical systems[M]//Dynamical Systems. Berlin, Heidelberg:Springer,1995: 1-43.
[18]LU K N, WANG B X. Wong-Zakai approximations and long term behavior of stochastic partial differential equations[J].Journal of Dynamics and Differential Equations, 2019,31: 1341-1371.
[1] 焦萌倩, 彭如月, 黄文韬, 蒋贵荣. 外激和参激作用下的三角翼飞行器滚转运动的随机响应[J]. 广西师范大学学报（自然科学版）, 2020, 38(5): 34-41.
[2] 佘连兵, 高云龙. 无界域上非自治Navier-Stokes方程的后向紧动力学[J]. 广西师范大学学报（自然科学版）, 2020, 38(1): 41-46.
[3] 黄开娇, 肖飞雁. 具有Beddington-DeAngelis型功能性反应的随机捕食—被捕食系统[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 32-40.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] 覃盈盈, 漆光超, 梁士楚. 凤眼莲组织浸提液对靖西海菜花种子萌发的影响[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 87 -92 .
[2] 王梦飞, 黄松. 广西西江经济带的城市旅游经济空间关联研究[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 144 -150 .
[3] 刘铭, 张双全, 何禹德. 基于改进SOM神经网络的异网电信用户细分研究[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 17 -24 .
[4] 温玉卓, 唐胜达, 邓国和. 随机环境下具有阈值分红策略的风险过程的破产时间分析[J]. 广西师范大学学报（自然科学版）, 2018, 36(3): 56 -62 .
[5] 邓亚彬,蒋品群,宋树祥. 新型低压微功耗伪差分跨导放大器设计[J]. 广西师范大学学报（自然科学版）, 2018, 36(1): 17 -24 .
[6] 孟齐,沈洪涛,毛立强,梁维刚,赵子珍,梁钊燕,赖鸣凤,黄保健,李世琢,何明,姜山. 用加速器质谱技术测定广西乐业天坑的暴露年龄[J]. 广西师范大学学报（自然科学版）, 2017, 35(1): 16 -20 .
[7] 许伦辉,尹诗德,刘易家. 基于模拟退火的自适应布谷鸟算法求解公交调度问题[J]. 广西师范大学学报（自然科学版）, 2018, 36(2): 1 -7 .
[8] 黄恒杰. 传感器中基于连通支配集的区域覆盖控制算法[J]. 广西师范大学学报（自然科学版）, 2016, 34(4): 19 -25 .
[9] 刘玉媛,曾上游. LTE同步技术频偏估计理论研究[J]. 广西师范大学学报（自然科学版）, 2016, 34(4): 32 -37 .
[10] 夏海英. 基于改进的SLIC区域合并的宫颈细胞图像分割[J]. 广西师范大学学报（自然科学版）, 2016, 34(4): 93 -100 .
版权所有 © 广西师范大学学报（自然科学版）编辑部
地址：广西桂林市三里店育才路15号　邮编：541004
电话：0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发