Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1040.37069
Dung, L.; Nicolaenko, B.
Exponential attractors in Banach spaces. (English)
[J] J. Dyn. Differ. Equations 13, No. 4, 791-806 (2001). ISSN 1040-7294; ISSN 1572-9222/e

Let $E$ be a Banach space, $U\subset E$ an open set and $S:U\rightarrow E$ a $C^1$-map. The authors consider the discrete dynamical system (DS) $\{S^n\}_{n=1}^{\infty}$ generated by $S$, extending the theory of exponential attractors from such DS in Hilbert space [{\it A. Eden, C. Foias, B. Nicolaenko} and {\it R. Temam}, Exponential attractors for dissipative evolution equations, Research in Applied Mathematics 37, Chichester: Wiley, Paris: Masson (1994; Zbl 0842.58056)] on Banach spaces. The following requirements are postulated: 1. the semiflow is $C^1$ in some absorbing ball, and 2. the linearized semiflow at every point inside the absorbing ball is splitting into the sum of a compact operator plus a contraction.
[Boris V. Loginov (Ul'yanovsk)]

MSC 2000:: *37L30 Attractors and their dimensions
35B41 Attractors
35Q30 Stokes and Navier-Stokes equations
47H20 Semigroups of nonlinear operators

Keywords: Banach spaces, discrete dynamical systems, exponential attractors

Citations: Zbl 0842.58056

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]