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非线性梁方程强全局吸引子的存在性 被引量:24

Existence of Strong Global Attractors for the Nonlinear Beam Equations
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摘要 非线性梁方程描述了桥面在竖直平面内的振动.作者利用文献[3]中给出的一种新的验证紧性的方法讨论了这类方程强解的全局吸引子. The nonlinear beam equations represent the viberation of the rode bed in downward direction. The authors discuss the global attractors of the strong solution by using a new method obtaining the compactness introduced in [3].
出处 《数学物理学报(A辑)》 CSCD 北大核心 2007年第5期941-948,共8页 Acta Mathematica Scientia
基金 国家自然科学基金(10471056) 数学天元基金(10626042) 甘肃省自然科学基金(3ZS061-A25-016) 西北师范大学科技创新工程基金(NWNU-KJCXGC-03-40)资助
关键词 全局吸引子 强解 梁方程 Global attractors Strong solution Beam equation.
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参考文献7

  • 1Medeiros L A. On a new class of nonlinear wave equations. J Math Anal Appl, 1979, 69: 252-262
  • 2De Brito E H. Decay estimates for the generalized damped extensible string and beam equations. Nonlinear Analysis, TMA, 1984, 8(12): 1489-1496
  • 3Ma Q F, Wang S H, Zhong C K. Necessary and sufficient conditions for the existence of global attractors for semigroup and applications. Indiana University Math J, 2002, 51(6): 1541-1559
  • 4Otto Vejvoda. Partial Differential Equations: Time-Periodic Solutions. The Hague, Boston, London: Martinus Nijhoff Publishers, 1982
  • 5Temam R. Infinite Dimensional Dynamical System in Mechanics and Physics (second edition). Berlin, Heidelberg, New York: Springer-Verlag, 1997
  • 6Ma Q Z, Zhong C K. Existence of strong global attractors for hyperbolic equation with linear memory. Applied Math Comp, 2004, 157(3)
  • 7Ma Q Z, Zhong C K. Global attractors of strong solutions to nonclassical diffusion equations. J Lanzhou University, 2004, 40(5)

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