Attractors for Equations of Mathematical Physics
( Colloquium Publications )
Publication series ：Colloquium Publications
Author： Vladimir V. Chepyzhov;Mark I. Vishik
Publisher： American Mathematical Society
Publication year： 2001
E-ISBN: 9781470431952
P-ISBN(Hardback): 9780821829509
Subject： O175.2 Partial Differential Equations
Keyword： 暂无分类
Language： ENG
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Attractors for Equations of Mathematical Physics
Description
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their solutions can be characterized by a very important notion of a global attractor of the equation. In this book, the authors study new problems related to the theory of infinite-dimensional dynamical systems that were intensively developed during the last 20 years. They construct the attractors and study their properties for various non-autonomous equations of mathematical physics: the 2D and 3D Navier-Stokes systems, reaction-diffusion systems, dissipative wave equations, the complex Ginzburg-Landau equation, and others. Since, as it is shown, the attractors usually have infinite dimension, the research is focused on the Kolmogorov $\varepsilon$-entropy of attractors. Upper estimates for the $\varepsilon$-entropy of uniform attractors of non-autonomous equations in terms of $\varepsilon$-entropy of time-dependent coefficients are proved. Also, the authors construct attractors for those equat
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