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Attractors of evolution equations /
Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionar...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Autres auteurs: | |
| Format: | Électronique eBook |
| Langue: | Inglés Ruso |
| Publié: |
Amsterdam ; New York : New York, N.Y.U.S.A. :
North-Holland ; Distributors for the U.S. and Canada, Elsevier Science Pub. Co.,
1992.
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| Collection: | Studies in mathematics and its applications ;
v. 25. |
| Sujets: | |
| Accès en ligne: | Texto completo Texto completo Texto completo |
| Résumé: | Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - & infin; all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - + & infin;, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - & infin; of solutions for evolutionary equations. |
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| Description: | Translation of: Attraktory �evol�i�u�t�sionnykh uravneni�i. |
| Description matérielle: | 1 online resource (x, 532 pages) |
| Bibliographie: | Includes bibliographical references (pages 505-526) and index. |
| ISBN: | 9780444890047 0444890041 9780080875460 0080875467 1281789577 9781281789570 9786611789572 661178957X |