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Infinite-Dimensional Dynamical Systems / Attractors and Methods

Boling Guo, Liming Ling, Yansheng Ma, Hui Yang (Autoren)

Buch | Hardcover

VIII, 405 Seiten

2018
De Gruyter (Verlag)
978-3-11-058699-2 (ISBN)

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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

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.

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

"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

Erscheinungsdatum	09.07.2018
Reihe/Serie	Infinite-Dimensional Dynamical Systems ; Volume 2
Zusatzinfo	30 b/w ill.
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	901 g
Themenwelt	Geschichte ► Allgemeine Geschichte ► 1918 bis 1945
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Applied • Applied mathematics • Differential Equations • KRIMINAL- • Lahti • Mathematical & Computational • Mathematics • Mathematik • Mechanics • Physics • Science • Strafrechtspolitik • STRWP27 • Theoretical and Mathematical Physics
ISBN-10	3-11-058699-1 / 3110586991
ISBN-13	978-3-11-058699-2 / 9783110586992
Zustand	Neuware