Asymptotic Behavior of Dissipative Systems
Asymptotic Behavior of Dissipative Systems
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DOI：
10.1090/surv/025
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发表时间：
1988-12
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影响因子：
--
通讯作者：
J. Hale
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文献类型：
--
作者：
J. Hale
离散动力系统：极限集不变集和渐近光滑映射的稳定性渐近光滑映射的例子耗散性和全局吸引子对参数的依赖性不动点定理相对于全局吸引子和Morse-Smale映射的稳定性全局吸引子的维数两个空间中的耗散性连续动力系统：极限集渐近光滑和$\alpha$-收缩半群不变集的稳定性耗散性和全局吸引子对参数的依赖周期过程斜积流梯度流耗散性在两个空间中吸引子上流的性质应用：延迟泛函微分方程扇形演化方程一个标量抛物方程Navier-Stokes方程中性泛函微分方程一些抽象的演化方程一维阻尼波动方程三维阻尼波动方程其他应用的备注依赖于参数和吸引子的近似。
Discrete dynamical systems: Limit sets Stability of invariant sets and asymptotically smooth maps Examples of asymptotically smooth maps Dissipativeness and global attractors Dependence on parameters Fixed point theorems Stability relative to the global attractor and Morse-Smale maps Dimension of the global attractor Dissipativeness in two spaces Continuous dynamical systems: Limit sets Asymptotically smooth and $\alpha$-contracting semigroups Stability of invariant sets Dissipativeness and global attractors Dependence on parameters Periodic processes Skew product flows Gradient flows Dissipativeness in two spaces Properties of the flow on the attractor Applications: Retarded functional differential equations Sectorial evolutionary equations A scalar parabolic equation The Navier-Stokes equation Neutral functional differential equations Some abstract evolutionary equations A one-dimensional damped wave equation A three-dimensional damped wave equation Remarks on other applications Dependence on parameters and approximation of the attractor.