Evolution Semigroups In Dynamical Systems And Differential Equations
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Evolution Semigroups In Dynamical Systems And Differential Equations
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Author : Carmen Chicone
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Evolution Semigroups In Dynamical Systems And Differential Equations written by Carmen Chicone and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The main theme of the book is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. The authors use a wide range of methods and offer a unique presentation. The authors give a unifying approach for a study of infinite-dimensional nonautonomous problems, which is based on the consistent use of evolution semigroups. This unifying idea connects various questions in stability of semigroups, infinite-dimensional hyperbolic linear skew-product flows, translation Banach algebras, transfer operators, stability radii in control theory, Lyapunov exponents, magneto-dynamics and hydro-dynamics. Thus the book is much broader in scope than existing books on asymptotic behavior of semigroups. Included is a solid collection of examples from different areas of analysis, PDEs, and dynamical systems. This is the first monograph where the spectral theory of infinite dimensional linear skew-product flows is described together with its connection to the multiplicative ergodic theorem; the same technique is used to study evolution semigroups, kinematic dynamos, and Ruelle operators; the theory of stability radii, an important concept in control theory, is also presented. Examples are included and non-traditional applications are provided.
Evolution Semigroups In Dynamical Systems And Differential Equations
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Author : Carmen Charles Chicone
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-05-22
Evolution Semigroups In Dynamical Systems And Differential Equations written by Carmen Charles Chicone and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-22 with MATHEMATICS categories.
The main theme of this work is the spectral theory for evolution operators and evolution semigroups, a subject tracing its origins to the classical results of J. Mather on hyperbolic dynamical systems and J. Howland on nonautonomous Cauchy problems. The authors use a wide range of methods and give a unifying approach for a study of infinite-dimensional nonautonomous problems, which is based on the consistent use of evolution semigroups.
Evolution Equations Semigroups And Functional Analysis
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Author : Brunello Terreni
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Evolution Equations Semigroups And Functional Analysis written by Brunello Terreni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi
Attractors For Semigroups And Evolution Equations
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Author : Olga A. Ladyzhenskaya
language : en
Publisher: Cambridge University Press
Release Date : 2022-06-09
Attractors For Semigroups And Evolution Equations written by Olga A. Ladyzhenskaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-09 with Mathematics categories.
First published 1992; Re-issued 2008; Reprinted with Introduction 2022.
Evolution Equations Semigroups And Functional Analysis
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Author : Alfredo Lorenzi
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Evolution Equations Semigroups And Functional Analysis written by Alfredo Lorenzi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi.
A Stability Technique For Evolution Partial Differential Equations
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Author : Victor A. Galaktionov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Stability Technique For Evolution Partial Differential Equations written by Victor A. Galaktionov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
* Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
Dynamical Systems And Evolution Equations
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Author : John A. Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Dynamical Systems And Evolution Equations written by John A. Walker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Computers categories.
This book grew out of a nine-month course first given during 1976-77 in the Division of Engineering Mechanics, University of Texas (Austin), and repeated during 1977-78 in the Department of Engineering Sciences and Applied Mathematics, Northwestern University. Most of the students were in their second year of graduate study, and all were familiar with Fourier series, Lebesgue integration, Hilbert space, and ordinary differential equa tions in finite-dimensional space. This book is primarily an exposition of certain methods of topological dynamics that have been found to be very useful in the analysis of physical systems but appear to be well known only to specialists. The purpose of the book is twofold: to present the material in such a way that the applications-oriented reader will be encouraged to apply these methods in the study of those physical systems of personal interest, and to make the coverage sufficient to render the current research literature intelligible, preparing the more mathematically inclined reader for research in this particular area of applied mathematics. We present only that portion of the theory which seems most useful in applications to physical systems. Adopting the view that the world is deterministic, we consider our basic problem to be predicting the future for a given physical system. This prediction is to be based on a known equation of evolution, describing the forward-time behavior of the system, but it is to be made without explicitly solving the equation.
Dynamics Of Evolutionary Equations
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Author : George R. Sell
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Dynamics Of Evolutionary Equations written by George R. Sell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entrée for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.
Evolutionary Equations With Applications In Natural Sciences
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Author : Jacek Banasiak
language : en
Publisher: Springer
Release Date : 2014-11-07
Evolutionary Equations With Applications In Natural Sciences written by Jacek Banasiak and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-07 with Mathematics categories.
With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory. Truly unique features of the book are: the first simultaneous presentation of two complementary approaches to fragmentation and coagulation problems, by weak compactness methods and by using semigroup techniques, comprehensive exposition of probabilistic methods of analysis of long term dynamics of dynamical systems, semigroup analysis of biological problems and cutting edge pattern formation theory. The book will appeal to postgraduate students and researchers specializing in applications of mathematics to problems arising in natural sciences and engineering.
Attractors Of Evolution Equations
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Author : A.V. Babin
language : en
Publisher: Elsevier
Release Date : 1992-03-09
Attractors Of Evolution Equations written by A.V. Babin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-09 with Mathematics categories.
Problems, ideas and notions from the theory of finite-dimensional dynamical systems have penetrated deeply into the theory of infinite-dimensional systems and partial differential equations. From the standpoint of the theory of the dynamical systems, many scientists have investigated the evolutionary equations of mathematical physics. Such equations include the Navier-Stokes system, magneto-hydrodynamics equations, reaction-diffusion equations, and damped semilinear wave equations. Due to the recent efforts of many mathematicians, it has been established that the attractor of the Navier-Stokes system, which attracts (in an appropriate functional space) as t - ∞ all trajectories of this system, is a compact finite-dimensional (in the sense of Hausdorff) set. Upper and lower bounds (in terms of the Reynolds number) for the dimension of the attractor were found. These results for the Navier-Stokes system have stimulated investigations of attractors of other equations of mathematical physics. For certain problems, in particular for reaction-diffusion systems and nonlinear damped wave equations, mathematicians have established the existence of the attractors and their basic properties; furthermore, they proved that, as t - +∞, an infinite-dimensional dynamics described by these equations and systems uniformly approaches a finite-dimensional dynamics on the attractor U, which, in the case being considered, is the union of smooth manifolds. This book is devoted to these and several other topics related to the behaviour as t - ∞ of solutions for evolutionary equations.