Large Time Behavior via the Method of ℓ-Trajectories
Large Time Behavior via the Method of ℓ-Trajectories
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DOI：
10.1006/jdeq.2001.4087
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发表时间：
2002-05
影响因子：
2.4
通讯作者：
J. Málek;D. Pražák
中科院分区：
文献类型：
--
作者：
J. Málek;D. Pražák
摘要 L-轨迹方法是在一般情况下作为研究非线性演化系统大时间行为的替代方法提出的。它可以成功地应用于解决方案缺乏规律性或主导椭圆算子是非线性的问题。在这里，我们专注于抛物型系统，并将该方法应用于抽象的一阶非线性耗散方程和一类与非线性流体力学相关的方程。在这两种情况下，我们都证明了有限维全局吸引子的存在和指数吸引子的存在。
Abstract The method of l-trajectories is presented in a general setting as an alternative approach to the study of the large-time behavior of nonlinear evolutionary systems. It can be successfully applied to the problems where solutions suffer from lack of regularity or when the leading elliptic operator is nonlinear. Here we concentrate on systems of a parabolic type and apply the method to an abstract nonlinear dissipative equation of the first order and to a class of equations pertinent to nonlinear fluid mechanics. In both cases we prove the existence of a finite-dimensional global attractor and the existence of an exponential attractor.