Nonautonomous Fractional Evolution Equations

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Nonautonomous Fractional Evolution Equations

Yong Zhou,Jia Wei He
Nonautonomous Fractional Evolution Equations Book PDF

Author : Yong Zhou,Jia Wei He
Publisher : Walter de Gruyter GmbH & Co KG
Page : 258 pages
File Size : 43,8 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 9783111391243

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Nonautonomous Fractional Evolution Equations by Yong Zhou,Jia Wei He Pdf

Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.

Theory of Fractional Evolution Equations

Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Theory of Fractional Evolution Equations Book PDF

Author : Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 45,8 Mb
Release : 2022-03-21
Category : Mathematics
ISBN : 9783110769272

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Theory of Fractional Evolution Equations by Yong Zhou,Bashir Ahmad,Ahmed Alsaedi Pdf

Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.

Functional Analytic Methods for Evolution Equations

Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Functional Analytic Methods for Evolution Equations Book PDF

Author : Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 45,9 Mb
Release : 2004-09-22
Category : Mathematics
ISBN : 3540230300

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Functional Analytic Methods for Evolution Equations by Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis Pdf

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Fractional-Order Equations and Inclusions

Michal Fečkan,JinRong Wang,Michal Pospíšil
Fractional Order Equations and Inclusions Book PDF

Author : Michal Fečkan,JinRong Wang,Michal Pospíšil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 383 pages
File Size : 53,7 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110521559

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Fractional-Order Equations and Inclusions by Michal Fečkan,JinRong Wang,Michal Pospíšil Pdf

This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Evolution Equations

Kaïs Ammari,Stéphane Gerbi
Evolution Equations Book PDF

Author : Kaïs Ammari,Stéphane Gerbi
Publisher : Cambridge University Press
Page : 205 pages
File Size : 51,8 Mb
Release : 2018
Category : Mathematics
ISBN : 9781108412308

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Evolution Equations by Kaïs Ammari,Stéphane Gerbi Pdf

The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.

Fractional Evolution Equations and Inclusions

Yong Zhou
Fractional Evolution Equations and Inclusions Book PDF

Author : Yong Zhou
Publisher : Academic Press
Page : 294 pages
File Size : 40,6 Mb
Release : 2016-02-05
Category : Mathematics
ISBN : 9780128047750

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Fractional Evolution Equations and Inclusions by Yong Zhou Pdf

Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spaces. Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature

Nonautonomous Dynamics

David N. Cheban
Nonautonomous Dynamics Book PDF

Author : David N. Cheban
Publisher : Springer Nature
Page : 434 pages
File Size : 47,5 Mb
Release : 2020-01-22
Category : Mathematics
ISBN : 9783030342920

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Nonautonomous Dynamics by David N. Cheban Pdf

This book emphasizes those topological methods (of dynamical systems) and theories that are useful in the study of different classes of nonautonomous evolutionary equations. The content is developed over six chapters, providing a thorough introduction to the techniques used in the Chapters III-VI described by Chapter I-II. The author gives a systematic treatment of the basic mathematical theory and constructive methods for Nonautonomous Dynamics. They show how these diverse topics are connected to other important parts of mathematics, including Topology, Functional Analysis and Qualitative Theory of Differential/Difference Equations. Throughout the book a nice balance is maintained between rigorous mathematics and applications (ordinary differential/difference equations, functional differential equations and partial difference equations). The primary readership includes graduate and PhD students and researchers in in the field of dynamical systems and their applications (control theory, economic dynamics, mathematical theory of climate, population dynamics, oscillation theory etc).

Stochastic Evolution Equations

Wilfried Grecksch,Constantin Tudor
Stochastic Evolution Equations Book PDF

Author : Wilfried Grecksch,Constantin Tudor
Publisher : De Gruyter Akademie Forschung
Page : 188 pages
File Size : 45,9 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015053939198

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Stochastic Evolution Equations by Wilfried Grecksch,Constantin Tudor Pdf

The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.

Evolution Equations, Semigroups and Functional Analysis

Brunello Terreni
Evolution Equations Semigroups and Functional Analysis Book PDF

Author : Brunello Terreni
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 51,5 Mb
Release : 2002
Category : Mathematics
ISBN : 3764367911

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Evolution Equations, Semigroups and Functional Analysis by Brunello Terreni Pdf

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

Nonautonomous Dynamical Systems in the Life Sciences

Peter E. Kloeden,Christian Pötzsche
Nonautonomous Dynamical Systems in the Life Sciences Book PDF

Author : Peter E. Kloeden,Christian Pötzsche
Publisher : Springer
Page : 314 pages
File Size : 45,7 Mb
Release : 2014-01-22
Category : Mathematics
ISBN : 9783319030807

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Nonautonomous Dynamical Systems in the Life Sciences by Peter E. Kloeden,Christian Pötzsche Pdf

Nonautonomous dynamics describes the qualitative behavior of evolutionary differential and difference equations, whose right-hand side is explicitly time dependent. Over recent years, the theory of such systems has developed into a highly active field related to, yet recognizably distinct from that of classical autonomous dynamical systems. This development was motivated by problems of applied mathematics, in particular in the life sciences where genuinely nonautonomous systems abound. The purpose of this monograph is to indicate through selected, representative examples how often nonautonomous systems occur in the life sciences and to outline the new concepts and tools from the theory of nonautonomous dynamical systems that are now available for their investigation.

Stabilization for Some Fractional-Evolution Systems

Kaïs Ammari,Fathi Hassine,Luc Robbiano
Stabilization for Some Fractional Evolution Systems Book PDF

Author : Kaïs Ammari,Fathi Hassine,Luc Robbiano
Publisher : Springer Nature
Page : 73 pages
File Size : 52,8 Mb
Release : 2022-10-19
Category : Mathematics
ISBN : 9783031173431

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Stabilization for Some Fractional-Evolution Systems by Kaïs Ammari,Fathi Hassine,Luc Robbiano Pdf

This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the abstract results of chapter 1 on concrete examples, and the third of which studies the stabilization of fractional evolution systems with memory.

Evolution Equations

Aleksandr Andreevich Pankov
Evolution Equations Book PDF

Author : Aleksandr Andreevich Pankov
Publisher : Unknown
Page : 340 pages
File Size : 55,7 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 153614259X

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Evolution Equations by Aleksandr Andreevich Pankov Pdf

This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.

Fractional-in-Time Semilinear Parabolic Equations and Applications

Ciprian G. Gal,Mahamadi Warma
Fractional in Time Semilinear Parabolic Equations and Applications Book PDF

Author : Ciprian G. Gal,Mahamadi Warma
Publisher : Springer Nature
Page : 193 pages
File Size : 52,6 Mb
Release : 2020-09-23
Category : Mathematics
ISBN : 9783030450434

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Fractional-in-Time Semilinear Parabolic Equations and Applications by Ciprian G. Gal,Mahamadi Warma Pdf

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.

Evolution Equations, Semigroups and Functional Analysis

Alfredo Lorenzi,Bernhard Ruf
Evolution Equations Semigroups and Functional Analysis Book PDF

Author : Alfredo Lorenzi,Bernhard Ruf
Publisher : Birkhäuser
Page : 404 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882217

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Evolution Equations, Semigroups and Functional Analysis by Alfredo Lorenzi,Bernhard Ruf Pdf

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.

Evolution Semigroups in Dynamical Systems and Differential Equations

Carmen Chicone,Yuri Latushkin
Evolution Semigroups in Dynamical Systems and Differential Equations Book PDF

Author : Carmen Chicone,Yuri Latushkin
Publisher : American Mathematical Soc.
Page : 375 pages
File Size : 40,7 Mb
Release : 1999
Category : Differentiable dynamical systems
ISBN : 9780821811856

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Evolution Semigroups in Dynamical Systems and Differential Equations by Carmen Chicone,Yuri Latushkin Pdf

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.