Infinite-dimensional Dynamical Systems: Attractor and Methods

by Boling Guo (Author)

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 fi rst volume is on the existence and properties for attractors and inertial manifolds. This volume highlights the use of modern analytical tools and methods such as the geometric measure method, center manifold theory in infinite dimensions, the Melnihov method, spectral analysis and so on for infinite-dimensional dynamical systems. The second volume includes the properties of global attractors, the calculation of discrete attractors, structures of small dissipative dynamical systems, and the existence and stability of solitary waves. ContentsDiscrete attractor and approximate calculation Some properties of global attractor Structures of small dissipative dynamical systems Existence and stability of solitary waves

Review
"The strength of this volume is the presentation of many examples of problems from mathematical physics governed by PDEs and the demonstration of how the theoretical results work for these particular problems. Moreover, the book contains many original results of the authors. The center of equilibrium of this volume, similar to the rst one, is placed around the estimates and calculations so that by studying them, one can learn how to apply the abstract results to particular equations."
Piotr Kalita in: Mathematical Reviews Clippings (07.2019), MR3823799

About the Author
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