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Uniform Attractors for Non-autonomous Brinkman-Forchheimer Equations with Delay 被引量：2

Uniform Attractors for Non-autonomous Brinkman–Forchheimer Equations with Delay
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摘要 In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force. In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force.
作者 Jum-Ran KANG Jong-Yeoul PARK
机构地区 Department of Mathematics Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2013年第5期993-1006,共14页 数学学报（英文版）
基金 Supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology(Grant No.2012R1A1A3011630)
关键词 Brinkman-Forchheimer equations uniform attractor DELAY translation compact Brinkman-Forchheimer equations, uniform attractor, delay, translation compact
分类号 O175 [理学—基础数学]
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参考文献22

  • 1Giorgi, T.: Derivation of the Forchheimer law via matched asymptotic expansions. Transp. Porous Media, 29, 191-206 (1997).
  • 2Whitaker, S.: The Forchheimer equation: A theoretical development. Transp. Porous Media, 25, 27-62 (1996).
  • 3Celebi, O., Kalantarov, V., Uaurlu, D.: On continuous dependence on solutions of the Brinkman Forchheimer equations. Appl. Math. Lett., 19, 801-807 (2006).
  • 4Franchi, F., Straughan, B.: Continuous dependence and decay for the Forchheimer equations. Proc. R. Soc. Lond. Set. A Math. Phys. Eng. Sci., 450, 3195-3202 (2003).
  • 5Payne, L. E., Song, J. C., Straughan, B.: Continuous dependence and convergence results for Brinkman and Forchheimer models with variable viscosity. Proc. R. Soc. Lond. Set. A Math. Phys. Eng. Sci., 455, 2173-2190 (1999).
  • 6Payne, L. E., Straughan, B.: Convergence and continuous dependence for the Brinkman-Forchheimer equations. Stud. Appl. Math., 102, 419-439 (1999).
  • 7Ugurlu, D.: On the existence of a global attractor for the Brinkman-Forchheimer equations. Nonlinear Anal., 68, 1986-1992 (2008).
  • 8Wang, B., Lin, S.: Existence of global attractors for the three-dimensional Brinkma~Forchheimer equation. Math. Methods Appl. Sei., 31, 1479-1495 (2008).
  • 9Babin, A. V., Vishik, M. I.: Attractors of Evolution Equations, North-Holland, Amsterdam, 1992.
  • 10Chueshov, I. D.: Introduction to the Theory of Infinite-Dimensional Dissipative Systems, Acta Scientific Publishing House, Kharkiv, Ukraine, 2002.

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Acta Mathematica Sinica,English Series
2013年 第5期

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