Infinite-Dimensional Dynamical Systems by James C Robinson
This book develops the theory of global attractors for a class of parabolic PDEs which includes reaction-diffusion equations and the Navier-Stokes equations, two examples that are treated in detail. A lengthy chapter on Sobolev spaces provides the framework that allows a rigorous treatment of existence and uniqueness of solutions for both linear time-independent problems (Poisson's equation) and the nonlinear evolution equations which generate the infinite-dimensional dynamical systems of the title. Attention then switches to the global attractor, a finite-dimensional subset of the infinite-dimensional phase space which determines the asymptotic dynamics. In particular, the concluding chapters investigate in what sense the dynamics restricted to the attractor are themselves 'finite-dimensional'. The book is intended as a didactic text for first year graduates, and assumes only a basic knowledge of Banach and Hilbert spaces, and a working understanding of the Lebesgue integral.-
Numerical Linear Algebra
-
Viscous Flow
-
Microhydrodynamics, Brownian Motion, and Complex Fluids
-
A First Course in the Numerical Analysis of Differential Equations
-
Perturbation Methods
-
Solitons
-
A First Course in Continuum Mechanics
-
Symmetry Methods for Differential Equations
-
Introduction to Magnetohydrodynamics
-
A Physical Introduction to Suspension Dynamics
-
Complex Variables
-
Nonlinear Systems
-
Stability, Instability and Chaos
-
Mathematical Models in the Applied Sciences
-
Introduction to Symmetry Analysis Paperback with CD-ROM
-
Complex Variables South Asian Edition
-
An Introduction to Stochastic Dynamics
-
Singularities: Formation, Structure, and Propagation
-
Stochastic Modelling of ReactionDiffusion Processes
-
Think Before You Compute
-
Introduction to Hydrodynamic Stability
-
Rarefied Gas Dynamics
-
Geometric and Topological Inference
-
Discrete Systems and Integrability
-
An Introduction to Polynomial and Semi-Algebraic Optimization
-
The Mathematics of Signal Processing
-
Iterative Methods in Combinatorial Optimization
-
High Speed Flow
-
Theory of Vortex Sound
-
Nonlinear Wave Processes in Acoustics
-
The Thermomechanics of Plasticity and Fracture
-
Backlund and Darboux Transformations
-
Boundary Integral and Singularity Methods for Linearized Viscous Flow
-
Maximum and Minimum Principles
-
Flow, Deformation and Fracture
-
An Introduction to Parallel and Vector Scientific Computation
-
The Kinematics of Mixing
-
Thinking about Ordinary Differential Equations
'… will certainly benefit young researchers entering the described field' Jan Cholewa, Zentralblatt MATH
'This impressive book offers an excellent, self-contained introduction to many important aspects of infinite-dimensional systems … At the outset, the author states that his aim was to produce a didactic text suitable or first-year graduate students. Unquestionably he has achieved his goal. This book should prove invaluable to mathematicians wishing to gain some knowledge of the dynamical-systems approach to dissipative partial differential equations that has been developed during the past 20 years, and should be essential reading for any graduate student starting out on a PhD in this area.' W. Lamb, Proceedings of the Edinburgh Mathematical Society
'The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion. A number of example problems are treated, and each chapter is followed by a series of problems whose solutions are available on the internet. … constitutes an excellent resource for researchers and advanced graduate students in applied mathematics, dynamical systems, nonlinear dynamics, and computational mechanics. Its acquisition by libraries is strongly recommended.' Applied Mechanics Reviews
'This impressive book offers an excellent, self-contained introduction to many important aspects of infinite-dimensional systems … At the outset, the author states that his aim was to produce a didactic text suitable or first-year graduate students. Unquestionably he has achieved his goal. This book should prove invaluable to mathematicians wishing to gain some knowledge of the dynamical-systems approach to dissipative partial differential equations that has been developed during the past 20 years, and should be essential reading for any graduate student starting out on a PhD in this area.' W. Lamb, Proceedings of the Edinburgh Mathematical Society
'The book is written clearly and concisely. It is well structured, and the material is presented in a rigorous, coherent fashion. A number of example problems are treated, and each chapter is followed by a series of problems whose solutions are available on the internet. … constitutes an excellent resource for researchers and advanced graduate students in applied mathematics, dynamical systems, nonlinear dynamics, and computational mechanics. Its acquisition by libraries is strongly recommended.' Applied Mechanics Reviews
| SKU | Unavailable |
| ISBN 13 | 9780521632041 |
| ISBN 10 | 0521632048 |
| Title | Infinite-Dimensional Dynamical Systems |
| Author | James C Robinson |
| Series | Cambridge Texts In Applied Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2001-04-23 |
| Number of pages | 480 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |