中国综合性科技类核心期刊(北大核心)

中国科学引文数据库来源期刊(CSCD)

美国《化学文摘》(CA)收录

美国《数学评论》(MR)收录

俄罗斯《文摘杂志》收录

Message Board

Respected readers, authors and reviewers, you can add comments to this page on any questions about the contribution, review, editing and publication of this journal. We will give you an answer as soon as possible. Thank you for your support!

Name
E-mail
Phone
Title
Content
Verification Code
Issue 4
Jul.  2020
Turn off MathJax
Article Contents
SONG An, WANG Xuan. Existence of random attractors for the Berger equation with white noise[J]. Journal of East China Normal University (Natural Sciences), 2020, (4): 51-63. doi: 10.3969/j.issn.1000-5641.201911011
Citation: SONG An, WANG Xuan. Existence of random attractors for the Berger equation with white noise[J]. Journal of East China Normal University (Natural Sciences), 2020, (4): 51-63. doi: 10.3969/j.issn.1000-5641.201911011

Existence of random attractors for the Berger equation with white noise

doi: 10.3969/j.issn.1000-5641.201911011
  • Received Date: 2019-02-27
    Available Online: 2020-07-20
  • Publish Date: 2020-07-20
  • 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.
  • loading
  • [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.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Article views (109) PDF downloads(4) Cited by()
    Proportional views

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return