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Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems

Global Periodic Attractors for a Class of Infinite Dimensional Dissipative Dynamical Systems
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摘要 In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary conditions. It is proved that in a certain parameter, for an arbitrary timeperiodic driving force, the system has a unique periodic solution attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of the global periodic attractor for abstract parabolic problems. In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary conditions. It is proved that in a certain parameter, for an arbitrary timeperiodic driving force, the system has a unique periodic solution attracting any bounded set exponentially in the phase space, which implies that the system behaves exactly as a one-dimensional system. We mention, in particular, that the obtained result can be used to prove the existence of the global periodic attractor for abstract parabolic problems.
作者 Hongyan Li
机构地区 College of Management
出处 《Advances in Pure Mathematics》 2013年第5期472-474,共3页 理论数学进展（英文）
关键词 DISSIPATIVE Equation GLOBAL PERIODIC ATTRACTOR One-Dimensional System Dissipative Equation Global Periodic Attractor One-Dimensional System
分类号 O1 [理学—基础数学]
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共引文献9

Advances in Pure Mathematics
2013年 第5期

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