Global Attractors In Abstract Parabolic Problems
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Global Attractors In Abstract Parabolic Problems
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Author : Jan W. Cholewa
language : en
Publisher:
Release Date : 2014-05-14
Global Attractors In Abstract Parabolic Problems written by Jan W. Cholewa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Global Attractors In Abstract Parabolic Problems
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Author : Jan W. Cholewa
language : en
Publisher: Cambridge University Press
Release Date : 2000-08-31
Global Attractors In Abstract Parabolic Problems written by Jan W. Cholewa 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 2000-08-31 with Mathematics categories.
This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.
Critical Parabolic Type Problems
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Author : Tomasz W. Dłotko
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-05-05
Critical Parabolic Type Problems written by Tomasz W. Dłotko and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-05 with Mathematics categories.
This self-contained book covers the theory of semilinear equations with sectorial operator going back to the studies of Yosida, Henry, and Pazy, which are deeply extended nowadays. The treatment emphasizes existence-uniqueness theory as a topic of functional analysis and examines abstract evolutionary equations, with applications to the Navier-Stokes system, the quasi-geostrophic equation, and fractional reaction-diffusion equations.
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems
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Author : Alexandre Carvalho
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-26
Attractors For Infinite Dimensional Non Autonomous Dynamical Systems written by Alexandre Carvalho 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 2012-09-26 with Mathematics categories.
The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.
Fractional In Time Semilinear Parabolic Equations And Applications
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Author : Ciprian G. Gal
language : en
Publisher: Springer Nature
Release Date : 2020-09-23
Fractional In Time Semilinear Parabolic Equations And Applications written by Ciprian G. Gal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Mathematics categories.
This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source, generally of arbitrary growth in the unknown function, a time derivative in the sense of Caputo and the presence of a large class of diffusion operators. The global regularity problem is then treated separately and the analysis is extended to some systems of fractional kinetic equations, including prey-predator models of Volterra–Lotka type and chemical reactions models, all of them possibly containing some fractional kinetics. Besides classical examples involving the Laplace operator, subject to standard (namely, Dirichlet, Neumann, Robin, dynamic/Wentzell and Steklov) boundary conditions, the framework also includes non-standard diffusion operators of "fractional" type, subject to appropriate boundary conditions. This book is aimed at graduate students and researchers in mathematics, physics, mathematical engineering and mathematical biology, whose research involves partial differential equations.
Handbook Of Dynamical Systems
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Author : A. Katok
language : en
Publisher: Elsevier
Release Date : 2005-12-17
Handbook Of Dynamical Systems written by A. Katok and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-17 with Mathematics categories.
This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Dynamics Of Quasi Stable Dissipative Systems
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Author : Igor Chueshov
language : en
Publisher: Springer
Release Date : 2015-09-29
Dynamics Of Quasi Stable Dissipative Systems written by Igor Chueshov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-29 with Mathematics categories.
This book is devoted to background material and recently developed mathematical methods in the study of infinite-dimensional dissipative systems. The theory of such systems is motivated by the long-term goal to establish rigorous mathematical models for turbulent and chaotic phenomena. The aim here is to offer general methods and abstract results pertaining to fundamental dynamical systems properties related to dissipative long-time behavior. The book systematically presents, develops and uses the quasi-stability method while substantially extending it by including for consideration new classes of models and PDE systems arising in Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate level. Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in Kharkov, Ukraine.
Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations
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Author : Sergey I Piskarev
language : en
Publisher: World Scientific
Release Date : 2023-07-05
Attractors Shadowing And Approximation Of Abstract Semilinear Differential Equations written by Sergey I Piskarev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-05 with Mathematics categories.
The book is devoted to some branches of the theory of approximation of abstract differential equations, namely, approximation of attractors in the case of hyperbolic equilibrium points, shadowing, and approximation of time-fractional semilinear problems.In this book, the most famous methods of several urgent branches of the theory of abstract differential equations scattered in numerous journal publications are systematized and collected together, which makes it convenient for the initial study of the subject and also for its use as a reference book. The presentation of the material is closed and accompanied by examples; this makes it easier to understand the material and helps beginners to quickly enter into the circle of ideas discussed.The book can be useful for specialists in partial differential equations, functional analysis, theory of approximation of differential equations, and for all researchers, students, and postgraduates who apply these branches of mathematics in their work.
Synchronization In Infinite Dimensional Deterministic And Stochastic Systems
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Author : Igor Chueshov
language : en
Publisher: Springer Nature
Release Date : 2020-07-29
Synchronization In Infinite Dimensional Deterministic And Stochastic Systems written by Igor Chueshov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-29 with Mathematics categories.
The main goal of this book is to systematically address the mathematical methods that are applied in the study of synchronization of infinite-dimensional evolutionary dissipative or partially dissipative systems. It bases its unique monograph presentation on both general and abstract models and covers several important classes of coupled nonlinear deterministic and stochastic PDEs which generate infinite-dimensional dissipative systems. This text, which adapts readily to advanced graduate coursework in dissipative dynamics, requires some background knowledge in evolutionary equations and introductory functional analysis as well as a basic understanding of PDEs and the theory of random processes. Suitable for researchers in synchronization theory, the book is also relevant to physicists and engineers interested in both the mathematical background and the methods for the asymptotic analysis of coupled infinite-dimensional dissipative systems that arise in continuum mechanics.
Advances In Mathematical Modeling Optimization And Optimal Control
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Author : Jean-Baptiste Hiriart-Urruty
language : en
Publisher: Springer
Release Date : 2016-05-19
Advances In Mathematical Modeling Optimization And Optimal Control written by Jean-Baptiste Hiriart-Urruty and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-19 with Mathematics categories.
This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.