带有白噪声的Berger方程随机吸引子的存在性

doi:10.3969/j.issn.1000-5641.201911011

华东师范大学学报（自然科学版） ›› 2020, Vol. 2020 ›› Issue (4): 51-63.doi: 10.3969/j.issn.1000-5641.201911011

带有白噪声的Berger方程随机吸引子的存在性

宋安, 汪璇

西北师范大学数学与统计学院,兰州 730070

收稿日期:2019-02-27 发布日期:2020-07-20
通讯作者: 汪璇,女,教授,研究方向为非线性微分方程和无穷维动力系统.E-mail:wangxuan@nwnu.edu.cn E-mail:wangxuan@nwnu.edu.cn
基金资助:
国家自然科学基金(11761062, 11561064, 11661071)

Existence of random attractors for the Berger equation with white noise

SONG An, WANG Xuan

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2019-02-27 Published:2020-07-20

摘要/Abstract

摘要： 研究了带有白噪声的Berger方程解的长时间动力学行为. 运用渐近先验估计技术和算子分解方法得到了Berger方程随机吸引子的存在性.

关键词: Berger方程, 随机吸引子, 算子分解, 存在性

Abstract: In this paper, we study the long-time behaviors of solutions for the Berger equation with white noise. By applying the asymptotic a priori estimates technique and the operator decomposition technique, the existence of random attractors is shown.

Key words: Berger equation, random attractor, operator decomposition, existence

中图分类号:

O175.27

宋安, 汪璇. 带有白噪声的Berger方程随机吸引子的存在性[J]. 华东师范大学学报（自然科学版）, 2020, 2020(4): 51-63.

SONG An, WANG Xuan. Existence of random attractors for the Berger equation with white noise[J]. Journal of East China Normal University(Natural Science), 2020, 2020(4): 51-63.

参考文献

[1] BERGER H M. A new approach to the analysis of large deflections of plates [J]. Appl Mech, 1955, 22: 465-472.
[2] DMITRIEVAŽN. On the theory of nonlinear oscillations of thin rectangular plates [J]. Izvestiya Vysshikh Uchebnykh Zavedeniǐ Matematika, 1978(8): 62-66.
[3] BALL J M. Stability theory for an extensible beam [J]. Journal of Differential Equations, 1973, 14(3): 399-418. DOI: 10.1016/0022-0396(73)90056-9.
[4] BIANCHI G, MARZOCCHI A. Asymptotic properties of solutions to semilinear damped equations for elastic beams [J]. Rivista di Matematica della Universitàdi Parma, 1996, 4: 241-258.
[5] SUN C, YANG L, DUAN J. Asymptotic behavior for a semilinear second order evolution equation [J]. Transactions of the American Mathematical Society, 2011, 363(11): 6085-6109. DOI: 10.1090/S0002-9947-2011-05373-0.
[6] CHOW P L. Asymptotic solutions of a nonlinear stochastic beam equation [J]. Discrete and Continuous Dynamical Systems (B), 2012, 6(4): 735-749.
[7] MARZOCCHI A, VUK E. Global attractor for damped semilinear elastic beam equations with memory [J]. Zeitschrift für Angewandte Mathematik und Physik, 2003, 54(2): 224-234. DOI: 10.1007/s000330300002.
[8] SELL G R, YOU Y C. Dynamics of Evolutionary Equations [M]. New York: Springer, 2002.
[9] CHUESHOV I, LASIECKA I. Long-Time Behavior of Second Order Evolution Equations with Nonlinear Damping [M]. Rhode Island: American Mathematical Society, 2008.
[10] NABOKA O. Synchronization of nonlinear oscillations of two coupling Berger plates [J]. Nonlinear Analysis Theory Methods and Applications, 2007, 67(4): 1015-1026. DOI: 10.1016/j.na.2006.06.034.
[11] YANG L, WANG X. Existence of attractors for the non-autonomous Berger equation with nonlinear damping [J]. Electronic Journal of Differential Equations, 2017, 2017(278): 1-14.
[12] MENG F J, WU J, ZHAO C. Time-dependent global attractor for extensible Berger equation [J]. Journal of Mathematical Analysis and Applications, 2019, 469(2): 1045-1069. DOI: 10.1016/j.jmaa.2018.09.050.
[13] CRAUEL H, FLANDOLI F. Attractors for random dynamical systems [J]. Probability Theory & Related Fields, 1994, 100(3): 365-393.
[14] CRAUEL H, DEBUSSCHE A, FLANDOLI F. Random attractors [J]. Journal of Dynamics & Differential Equations, 1997, 9(2): 307-341.
[15] ARNOLD L. Random Dynamical Systems [M]. New York: Springer-Verlag, 1998.
[16] CRAURL H. Random point attractors versus random set attractors [J]. Journal of the London Mathematical Society, 2001, 63(2): 413-427. DOI: 10.1017/S0024610700001915.
[17] LI Y R, GUO B L. Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction-diffusion equations [J]. Journal of Differential Equations, 2008, 245: 1775-1800. DOI: 10.1016/j.jde.2008.06.031.
[18] PAZY A. Semigroups of Linear Operators and Applications to Partial Differential Equations [M]. New York: Springer-Verlag, 1983.
[19] MA Q, XU L. Random attractors for the extensible suspension bridge equation with white noise [J]. Computers and Mathematics with Applications, 2015, 70(12): 2895-2903. DOI: 10.1016/j.camwa.2015.09.029.
[20] XU L, MA Q Z. Existence of random attractors for the floating beam equation with strong damping and white noise [J]. Boundary Value Problems, 2015, 2015(1): 126. DOI: 10.1186/s13661-015-0391-8.

带有白噪声的Berger方程随机吸引子的存在性

Existence of random attractors for the Berger equation with white noise

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 10

编辑推荐

Metrics

本文评价

[1]	王怡, 马巧珍. 带有线性记忆的plate方程随机吸引子的上半连续性[J]. 华东师范大学学报(自然科学版), 2019, 2019(1): 32-38.
[2]	晋守博, 张祖峰. 一类波动方程整体解的存在性与不存在性[J]. 华东师范大学学报(自然科学版), 2018, 2018(2): 1-10.
[3]	胡弟弟, 汪璇. 记忆型抽象发展方程时间依赖吸引子的存在性[J]. 华东师范大学学报(自然科学版), 2018, 2018(1): 35-49.
[4]	徐红梅; 徐伟. 一类无粘性项BBM-Burgers方程解的整体存在性和衰减估计[J]. 华东师范大学学报(自然科学版), 2016, 2016(6): 71-76.
[5]	李细柳, 穆春来, 曾嵘, 周寿明. 非线性~$p(x)$-Kirchhoff~方程在动态边界条件下的非全局存在性~[J]. 华东师范大学学报(自然科学版), 2013, 2013(3): 149-163，175.
[6]	姚庆六. 一类奇异三阶常微分方程的正解存在性与多解性[J]. 华东师范大学学报(自然科学版), 2010, 2010(3): 113-118.
[7]	田德建;江龙;邓芳. 系数为广义左Lipschitz的倒向随机微分方程解的存在性[J]. 华东师范大学学报(自然科学版), 2010, 2010(3): 119-125.
[8]	王丽华;. 非线性边界条件下的线性波动方程的解[J]. 华东师范大学学报(自然科学版), 2009, 2009(4): 78-81.
[9]	姚庆六. 非线性Sturm-Liouville问题的一个正解存在定理[J]. 华东师范大学学报(自然科学版), 2009, 2009(1): 32-36.
[10]	刘兴波. 非线性方程极限环的存在唯一性[J]. 华东师范大学学报(自然科学版), 2004, 2004(3): 1-5，28.