Attractors and Inertial Manifolds

1. Auflage 2018
ISBN: 978-3-11-054925-6
Verlag: De Gruyter

Buch, Englisch, Band Volume 1, 430 Seiten, Format (B × H): 175 mm x 246 mm, Gewicht: 917 g

Reihe: Infinite-Dimensional Dynamical Systems

This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents
Attractor and its dimension estimation
Inertial manifold
The approximate inertial manifold

Zielgruppe

Researchers and graduate students in mathematics and physics.

Autoren/Hrsg.

Guo, Boling

Yang, Hui

Ling, Liming

Ma, Yansheng

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Table of contents
Chapter 1 The Attractor and Its Estimation of Dimension
Chapter 2 Inertial Manifold
Chapter 3 The Approximate Inertial Manifold
Chapter 4 Discrete Attractor and Approximate Calculation
Chapter 5 Some Properties of Global Attractor
Chapter 6 The dynamics with small dissipation
Chapter 7 Existence and Stability of Solitary Waves
Chapter 8 Numerical computation method for some nonlinear evolution equations
References

Über Autor(innen)

B. Guo, Inst. of Appl. Phys. & Comp. Math.; L. Ling, South China U. of Tech.; Y. Ma, Northeast Normal U.; H. Yang, Yunnan Normal U.