Pullback attractors for generalized Korteweg-de Vries-Burgers equations

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Abstract

In this paper, we study the long-time behavior of solutions to the generalized Korteweg-de Vries-Burgers equation of the form. ut+uxxx+(g(u))x+γu-νuxx=f(t),where ν≥0,γ>0. We prove the existence of pullback attractors Aν in H1(R) for this equation in both cases ν = 0 and ν≥ 0. Moreover, the upper semicontinuity of the pullback attractors at ν = 0 is also investigated. © 2011 Elsevier Inc.

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Anh, C. T., & Bao, T. Q. (2012). Pullback attractors for generalized Korteweg-de Vries-Burgers equations. Journal of Mathematical Analysis and Applications, 388(2), 899–912. https://doi.org/10.1016/j.jmaa.2011.10.036

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