Topological Structure Of The Solution Set For Evolution Inclusions

Author : Yong Zhou,Rong-Nian Wang,Li Peng
Publisher : Springer
Page : 269 pages
File Size : 41,5 Mb
Release : 2017-10-31
Category : Mathematics
ISBN : 9789811066566

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Topological Structure of the Solution Set for Evolution Inclusions by Yong Zhou,Rong-Nian Wang,Li Peng Pdf

This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems; evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.

Author : J. Andres,Lech Górniewicz
Publisher : Springer Science & Business Media
Page : 771 pages
File Size : 40,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401704076

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Topological Fixed Point Principles for Boundary Value Problems by J. Andres,Lech Górniewicz Pdf

The book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topological fixed point theory in non-metric spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Therefore, three appendices concerning almost-periodic and derivo-periodic single-valued (multivalued) functions and (multivalued) fractals are supplied to the main three chapters.

Author : Yong Zhou
Publisher : Academic Press
Page : 294 pages
File Size : 54,7 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

Author : Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 255 pages
File Size : 47,5 Mb
Release : 2022-03-21
Category : Technology & Engineering
ISBN : 9783110769364

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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.

Author : Shouchuan Hu,Nikolaos S. Papageorgiou
Publisher : Springer Science & Business Media
Page : 941 pages
File Size : 47,5 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781461546658

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Handbook of Multivalued Analysis by Shouchuan Hu,Nikolaos S. Papageorgiou Pdf

In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 430 pages
File Size : 40,8 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822612

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 53,6 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.

Author : Yong Zhou,Jia Wei He
Publisher : Walter de Gruyter GmbH & Co KG
Page : 258 pages
File Size : 46,7 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.

Author : Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab
Publisher : Walter de Gruyter
Page : 474 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783110293562

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Solution Sets for Differential Equations and Inclusions by Smaïl Djebali,Lech Górniewicz,Abdelghani Ouahab Pdf

This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.

Author : Yong Zhou
Publisher : World Scientific
Page : 516 pages
File Size : 43,9 Mb
Release : 2023-10-06
Category : Mathematics
ISBN : 9789811271700

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Basic Theory Of Fractional Differential Equations (Third Edition) by Yong Zhou Pdf

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Author : Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie
Publisher : CRC Press
Page : 322 pages
File Size : 54,7 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315351681

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Delay Differential Evolutions Subjected to Nonlocal Initial Conditions by Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie Pdf

Filling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions. After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial conditions, examine delay evolution inclusions, and extend some results to the multivalued case of reaction-diffusion systems. The book concludes with results on viability for nonlocal evolution inclusions.

Author : Anonim
Publisher : Unknown
Page : 994 pages
File Size : 42,6 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015082440887

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Mathematical Reviews by Anonim Pdf

Author : Mikhail Z. Zgurovsky,Valery S. Mel'nik,Pavlo O. Kasyanov
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 46,5 Mb
Release : 2010-10-01
Category : Mathematics
ISBN : 9783642138782

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Evolution Inclusions and Variation Inequalities for Earth Data Processing II by Mikhail Z. Zgurovsky,Valery S. Mel'nik,Pavlo O. Kasyanov Pdf

Here, the authors present modern mathematical methods to solve problems of differential-operator inclusions and evolution variation inequalities which may occur in fields such as geophysics, aerohydrodynamics, or fluid dynamics. For the first time, they describe the detailed generalization of various approaches to the analysis of fundamentally nonlinear models and provide a toolbox of mathematical equations. These new mathematical methods can be applied to a broad spectrum of problems. Examples of these are phase changes, diffusion of electromagnetic, acoustic, vibro-, hydro- and seismoacoustic waves, or quantum mechanical effects. This is the second of two volumes dealing with the subject.

Author : A. Canada,P. Drabek,A. Fonda
Publisher : Elsevier
Page : 752 pages
File Size : 41,6 Mb
Release : 2006-08-21
Category : Mathematics
ISBN : 0080463819

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Handbook of Differential Equations: Ordinary Differential Equations by A. Canada,P. Drabek,A. Fonda Pdf

This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields

Author : Mikhail Z. Zgurovsky,Pavlo O. Kasyanov,Oleksiy V. Kapustyan,José Valero,Nina V. Zadoianchuk
Publisher : Springer Science & Business Media
Page : 368 pages
File Size : 43,7 Mb
Release : 2012-05-22
Category : Mathematics
ISBN : 9783642285127

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Evolution Inclusions and Variation Inequalities for Earth Data Processing III by Mikhail Z. Zgurovsky,Pavlo O. Kasyanov,Oleksiy V. Kapustyan,José Valero,Nina V. Zadoianchuk Pdf

In this sequel to two earlier volumes, the authors now focus on the long-time behavior of evolution inclusions, based on the theory of extremal solutions to differential-operator problems. This approach is used to solve problems in climate research, geophysics, aerohydrodynamics, chemical kinetics or fluid dynamics. As in the previous volumes, the authors present a toolbox of mathematical equations. The book is based on seminars and lecture courses on multi-valued and non-linear analysis and their geophysical application.