Attractors of evolution equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Amsterdam
North-Holland
1992
|
| Series: | Studies in mathematics and its applications
v. 25 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Translation of: Attraktory ėvoli͡ut͡sionnykh uravneniĭ 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 Includes bibliographical references (p. 505-526) and index |
| Physical Description: | 1 Online-Ressource (x, 532 p.) |
| ISBN: | 9780444890047 0444890041 |
Staff View
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| 500 | |a 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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Record in the Search Index
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| spelling | Babin, A. V., (Anatoliĭ Vladimirovich) Verfasser aut Attraktory ėvoli͡ut͡sionnykh uravneniĭ Attractors of evolution equations A.V. Babin and M.I. Vishik Amsterdam North-Holland 1992 1 Online-Ressource (x, 532 p.) txt rdacontent c rdamedia cr rdacarrier Studies in mathematics and its applications v. 25 Translation of: Attraktory ėvoli͡ut͡sionnykh uravneniĭ 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 Includes bibliographical references (p. 505-526) and index Navier-Stokes, Équations de / Solutions numériques Navier-Stokes, équations / Solutions numériques ram Attractors (Mathematics) fast Navier-Stokes equations / Numerical solutions fast Navier-Stokes equations Numerical solutions Attractors (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 gnd rswk-swf Attraktor (DE-588)4140563-8 gnd rswk-swf Evolutionsgleichung (DE-588)4129061-6 gnd rswk-swf Navier-Stokes-Gleichung (DE-588)4041456-5 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Evolutionsgleichung (DE-588)4129061-6 s Attraktor (DE-588)4140563-8 s 2\p DE-604 Vishik, M. I. Sonstige oth http://www.sciencedirect.com/science/book/9780444890047 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Babin, A. V., (Anatoliĭ Vladimirovich) Attractors of evolution equations Navier-Stokes, Équations de / Solutions numériques Navier-Stokes, équations / Solutions numériques ram Attractors (Mathematics) fast Navier-Stokes equations / Numerical solutions fast Navier-Stokes equations Numerical solutions Attractors (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Attraktor (DE-588)4140563-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| subject_GND | (DE-588)4128130-5 (DE-588)4041456-5 (DE-588)4140563-8 (DE-588)4129061-6 |
| title | Attractors of evolution equations |
| title_alt | Attraktory ėvoli͡ut͡sionnykh uravneniĭ |
| title_auth | Attractors of evolution equations |
| title_exact_search | Attractors of evolution equations |
| title_full | Attractors of evolution equations A.V. Babin and M.I. Vishik |
| title_fullStr | Attractors of evolution equations A.V. Babin and M.I. Vishik |
| title_full_unstemmed | Attractors of evolution equations A.V. Babin and M.I. Vishik |
| title_short | Attractors of evolution equations |
| title_sort | attractors of evolution equations |
| topic | Navier-Stokes, Équations de / Solutions numériques Navier-Stokes, équations / Solutions numériques ram Attractors (Mathematics) fast Navier-Stokes equations / Numerical solutions fast Navier-Stokes equations Numerical solutions Attractors (Mathematics) Numerisches Verfahren (DE-588)4128130-5 gnd Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Attraktor (DE-588)4140563-8 gnd Evolutionsgleichung (DE-588)4129061-6 gnd |
| topic_facet | Navier-Stokes, Équations de / Solutions numériques Navier-Stokes, équations / Solutions numériques Attractors (Mathematics) Navier-Stokes equations / Numerical solutions Navier-Stokes equations Numerical solutions Numerisches Verfahren Navier-Stokes-Gleichung Attraktor Evolutionsgleichung |
| url | http://www.sciencedirect.com/science/book/9780444890047 |
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