Babin A.V. (EN) — Attractors of Evolution Equations

Тут можно читать онлайн книгу Babin A.V. (EN) - Attractors of Evolution Equations - бесплатно полную версию (целиком). Жанр книги: Иностранная литература. Вы можете прочесть полную версию (весь текст) онлайн без регистрации и смс на сайте Lib-King.Ru (Либ-Кинг) или прочитать краткое содержание, аннотацию (предисловие), описание и ознакомиться с отзывами (комментариями) о произведении.

Attractors of Evolution Equations
Язык книги: Английский
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Attractors of Evolution Equations - описание и краткое содержание, автор Babin A.V. (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

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 - 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 - +, 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 - of solutions for evolutionary equations.

Attractors of Evolution Equations - читать онлайн бесплатно полную версию (весь текст целиком)

Attractors of Evolution Equations - читать книгу онлайн бесплатно, автор Babin A.V. (EN)

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