کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
840629 | 908486 | 2012 | 21 صفحه PDF | دانلود رایگان |

This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like semigroups in a general Banach space in terms of the maximum of the dimension of the local unstable manifolds of the isolated invariant sets, Lipschitz properties of the semigroup and the rate of exponential attraction. We also generalize this result for some special evolution processes, introducing a concept of Morse decomposition with pullback attractivity. Under suitable assumptions, if (A,A∗)(A,A∗) is an attractor–repeller pair for the attractor AA of a semigroup {T(t):t≥0}{T(t):t≥0}, then the fractal dimension of AA can be estimated in terms of the fractal dimension of the local unstable manifold of A∗A∗, the fractal dimension of AA, the Lipschitz properties of the semigroup and the rate of the exponential attraction. The ingredients of the proof are the notion of generalized gradient-like semigroups and their regular attractors, Morse decomposition and a fine analysis of the structure of the attractors. As we said previously, we generalize this result for some evolution processes using the same basic ideas.
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 75, Issue 14, September 2012, Pages 5702–5722