Infinite-Dimensional Dynamical Systems in Mechanics and Physics - Rilegato

Temam, Roger

 
9780387966380: Infinite-Dimensional Dynamical Systems in Mechanics and Physics
Rilegato
ISBN 10: 0387966382 ISBN 13: 9780387966380
Casa editrice: Springer Verlag, 1988

Sinossi

The study of nonlinear dynamics is a fascinating question which is at the very heart of the understanding of many important problems of the natural sciences. Two of the oldest and most notable classes of problems in nonlinear dynamics are the problems of celestial mechanics, especially the study of the motion of bodies in the solar system, and the problems of turbulence in fluids. Both phenomena have attracted the interest of scientists for a long time; they are easy to observe, and lead to the formation and development of complicated patterns that we would like to understand. The first class of problems are of finite dimensions, the latter problems have infinite dimensions, the dimensions here being the number of parameters which is necessary to describe the configuration of the system at a given instant of time. Besides these problems, whose observation is accessible to the layman as well as to the scientist, there is now a broad range of nonlinear turbulent phenomena (of either finite or infinite dimensions) which have emerged from recent developments in science and technology, such as chemical dynamics, plasma physics and lasers, nonlinear optics, combustion, mathematical economy, robotics, . . . . In contrast to linear systems, the evolution of nonlinear systems obeys complicated laws that, in general, cannot be arrived at by pure intuition or by elementary calculations.

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Contenuti

Contents: General Introduction. The User's Guide. General Results and Concepts on Invariant Sets and Attractors.- Elements of Functional Analysis.- Attractors of the Dissipative Evolution Equation of the First Order in Time: Reaction-Diffusion Equations. Fluid Mechanics and Pattern Formation Equations.- Attractors of Dissipative Wave Equations.- Lyapunov Exponents and Dimension of Attractors.- Explicit Bounds on the Number of Degrees of Freedom and the Dimension of Attractors of Some Physical Systems.- Non- Well-Posed Problems, Unstable Manifolds, Lyapunov Functions, and Lower Bounds on Dimensions.- The Cone and Squeezing Properties. Inertial Monifolds.- Appendix: Collective Sobolev Inequalities.- Bibliography.- Index.

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Editore
Springer Verlag
Data di pubblicazione
1988
Lingua
Inglese
ISBN 10 
0387966382
ISBN 13 
9780387966380
Rilegatura
Copertina rigida
Numero edizione
1
Numero di pagine
516
Contatto del produttore
non disponibile
Persona responsabile
CMN Printpool Inh. Mathis Neumann
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Altre edizioni note dello stesso titolo

9781461206460: Infinite-Dimensional Dynamical Systems in Mechanics and Physics

Edizione in evidenza

ISBN 10:  1461206464 ISBN 13:  9781461206460
Casa editrice: Springer, 2014
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