Existence of random attractors for the Berger equation with white noise

doi:10.3969/j.issn.1000-5641.201911011

Abstract

CLC Number:

O175.27

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.

[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.

Existence of random attractors for the Berger equation with white noise

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 13

Recommended Articles

Metrics

Comments

[1]	WANG Yi, MA Qiao-zhen. The upper semi-continuity of the random attractor of the plate equation with linear memory [J]. Journal of East China Normal University(Natural Sc, 2019, 2019(1): 32-38.
[2]	JIN Shou-bo, ZHANG Zu-feng. Existence and non-existence of global solutions for the wave equations [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(2): 1-10.
[3]	HU Di-di, WANG Xuan. The existence of time-dependent attractors for abstract evolution equations with fading memory [J]. Journal of East China Normal University(Natural Sc, 2018, 2018(1): 35-49.
[4]	XU Hong-mei, XU Wei. Global existence and decay estimate of the solution for a BBM-Burgers equation without viscosity [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(6): 71-76.
[5]	LIAO Jun-xia, FAN Sheng-jun. Lp solutions of BSDEs with weakly monotonic and uniformly continuous generators [J]. Journal of East China Normal University(Natural Sc, 2016, 2016(6): 77-87.
[6]	XU Shao-Ya, FAN Sheng-Jun. A general existence and uniqueness result on multidimensional BSDEs [J]. Journal of East China Normal University(Natural Sc, 2015, 2015(1): 51-60.
[7]	LI Xi-liu, MU Chun-lai, ZENG Rong, ZHOU Shou-ming. Global nonexistence for nonlinear $p(x)$-Kirchhoff systems with dynamic boundary conditions [J]. Journal of East China Normal University(Natural Sc, 2013, 2013(3): 149-163，175.
[8]	XIAO Li-shun,LI Hui-ying,FAN Sheng-jun. One-dimensional BSDEs with monotonic, H\"{o}lder continuous and Integrable parameters [J]. Journal of East China Normal University(Natural Sc, 2012, 2012(1): 130-137.
[9]	YAO Qing-liu. Existence and multiplicity of positive solutions to a class of singular third-order ordinary differential equations [J]. Journal of East China Normal University(Natural Sc, 2010, 2010(3): 113-118.
[10]	TIAN De-jian;JIANG Long;DENG Fang. On existence of solutions to backward stochastic differential equation with generalized left-Lipschitz coefficients [J]. Journal of East China Normal University(Natural Sc, 2010, 2010(3): 119-125.
[11]	WANG Li-hua;. Solutions to a linear wave equation with nonlinear\\[5pt] boundary conditions [J]. Journal of East China Normal University(Natural Sc, 2009, 2009(4): 78-81.
[12]	YAO Qing-liu. Existence theorem of positive solution to a nonlinear Sturm-Liouville problem (Chinese) [J]. Journal of East China Normal University(Natural Sc, 2009, 2009(1): 32-36.
[13]	LIU Xing-bo. Existence and Uniqueness of Limit Cycle for A Nonlinear Equation [J]. Journal of East China Normal University(Natural Sc, 2004, 2004(3): 1-5，28.