An Introduction to Infinite Dimensional Dynamical Systems - Geometric Theory PDF Download

Author: J.K. Hale
Publisher: Springer Science & Business Media
ISBN: 1475744935
Category : Mathematics
Languages : en
Pages : 203

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Including: An Introduction to the Homotopy Theory in Noncompact Spaces

Author: Jack K. Hale
Publisher: Springer Science & Business Media
ISBN: 9780387909318
Category : Mathematics
Languages : en
Pages : 195

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Author: Jack K. Hale
Publisher: Springer Science & Business Media
ISBN: 0387954635
Category : Mathematics
Languages : en
Pages : 287

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State-of-the-art in qualitative theory of functional differential equations; Most of the new material has never appeared in book form and some not even in papers; Second edition updated with new topics and results; Methods discussed will apply to other equations and applications

Author: James C. Robinson
Publisher: Cambridge University Press
ISBN: 9780521632041
Category : Mathematics
Languages : en
Pages : 488

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Book Description
This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject. As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research problems. Since the subject is relatively new, this is the first book to attempt to treat these various topics in a unified and didactic way. It is intended to be suitable for first year graduate students.

Author: Roger Temam
Publisher: Springer Science & Business Media
ISBN: 1461206456
Category : Mathematics
Languages : en
Pages : 670

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In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

Author: James Robinson
Publisher: Springer Science & Business Media
ISBN: 9780792369769
Category : Mathematics
Languages : en
Pages : 236

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Proceedings of the NATO Advanced Study Institute, Cambridge, UK, 21 August-1 September 1995

Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 1461208211
Category : Mathematics
Languages : en
Pages : 417

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Book Description
The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.

Author: Catherine Sulem
Publisher: Springer Science & Business Media
ISBN: 0387227687
Category : Mathematics
Languages : en
Pages : 363

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Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

Author: J.K. Kevorkian
Publisher: Springer Science & Business Media
ISBN: 1461239680
Category : Mathematics
Languages : en
Pages : 642

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Book Description
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Author: Frank C. Hoppensteadt
Publisher: Springer Science & Business Media
ISBN: 1461218284
Category : Mathematics
Languages : en
Pages : 404

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Book Description
Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.