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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 576087, 8 pages
http://dx.doi.org/10.1155/2014/576087
Research Article

A Stochastic Weakly Damped, Forced KdV-BO Equation

Department of Mathematics, Tongji University, Shanghai 200092, China

Received 14 January 2014; Revised 13 April 2014; Accepted 13 April 2014; Published 5 May 2014

Academic Editor: Tonghua Zhang

Copyright © 2014 Guolian Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. B. Guo and Z. Huo, “The well-posedness of the Korteweg-de Vries-Benjamin-Ono equation,” Journal of Mathematical Analysis and Applications, vol. 295, no. 2, pp. 444–458, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. F. Linares, “L2 global well-posedness of the initial value problem associated to the Benjamin equation,” Journal of Differential Equations, vol. 152, no. 2, pp. 377–393, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. R. L. Herman, “The stochastic, damped KdV equation,” Journal of Physics A: Mathematical and General, vol. 23, no. 7, pp. 1063–1084, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Scalerandi, A. Romano, and C. A. Condat, “Korteweg-de Vries solitons under additive stochastic perturbations,” Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 58, no. 4, pp. 4166–4173, 1998. View at Google Scholar · View at Scopus
  5. B. Guo and Z. Huo, “The global attractor of the damped, forced generalized Korteweg de Vries-Benjamin-Ono equation in L2,” Discrete and Continuous Dynamical Systems A, vol. 16, no. 1, pp. 121–136, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Wang and B. Guo, “Well-posedness of stochastic Korteweg-de Vries-Benjamin-Ono equation,” Frontiers of Mathematics in China, vol. 5, no. 1, pp. 161–177, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. L. Arnold, Random Dynamical Systems, Springer, Berlin, Germany, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  8. H. Crauel and F. Flandoli, “Attractors for random dynamical systems,” Probability Theory and Related Fields, vol. 100, no. 3, pp. 365–393, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Crauel, A. Debussche, and F. Flandoli, “Random attractors,” Journal of Dynamics and Differential Equations, vol. 9, no. 2, pp. 307–341, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. G. da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. de Bouard and A. Debussche, “On the stochastic Korteweg-de Vries equation,” Journal of Functional Analysis, vol. 154, no. 1, pp. 215–251, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J.-M. Ghidaglia, “Finite-dimensional behavior for weakly damped driven Schrödinger equations,” Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, vol. 5, no. 4, pp. 365–405, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. R. Rosa, “The global attractor of a weakly damped, forced Korteweg-de Vries equation in H1(),” Matemática Contemporânea, vol. 19, pp. 129–152, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet