Convergent Families of Approximate Inertial Manifolds for Nonautonomous Evolution Equations
-
Abstract: In this paper,the long time behavior of nonautonomous infinite dimensional dynamical systems is studied.A family of convergent approximate inertial manifolds for a class of evolution equations has been constructed when the spectral gap condition is satisfied.
-
[1] R.Temam,Infinite Dimensional Dynamical Systems in Mechanics and Physics,Springer-Verlag,New York(1988). [2] J.Hale,Asymptotic behavior of dissipative systems,Ma th.Surveys and Monographs,25,Amer.Math.Soc.Providence,Rhode Island(1988). [3] A.R.Bernal,I nertial manifold for dissipative semiflows in Banach spaces,Applicable Analysis,37(1990),95-141. [4] A.Debussche and R.Temam,Convergent families of approximate inertial manifold,J.Math.Pure Appl.,73(5)(1994),489-522. [5] C.M.Dafermos,Semi-flows associated with compact and uniform processes,Math.Systems Theory,8(1974),142-149. [6] G.R.Sell,Non-autonomous differential equations and to pological dynamics,Ⅰ,Ⅱ,Trans.Amer.Math.Soc.,127(1967),241-263. [7] V.V.Chepyzhov and M.I.Vishik,Attractors of nonautonomous dynamical systems and their dimension,J.Math.Pure Appl.,73(3)(1994),297-333. [8] T.Gill and W.Zachary,Dimensionabity of invariant sets for nonautonomous processes,SIAM J.Math.Anal.,23(5)(1992),1204-1229. [9] A.Haraux,Attractors of asymptotically compact process and applications to nonlinear partial differential equations,Comm.Partial Differential Equations,13(1988),1383-1414. [10] M.W.Smiley,Global attractors and approximate inertial manifold for nonautonomous dissipative equations,Applicable Analysis,50(3-4)(1993),217-241. [11] M.W.Smiley,Regularity and asymptotic behavior of solutions of nonautonomous differential equations,Journal of Dynamics and Differential Equations,7(2)(1995),237-262. [12] 王宗信、范先令、朱正佑,非自治无穷维动力系统的惯性流形,应用数学和力学,19(7)(1998),649-657.
点击查看大图
计量
- 文章访问数: 1751
- HTML全文浏览量: 32
- PDF下载量: 530
- 被引次数: 0