Download or read book Semigroups Associated with Dissipative Systems written by Z Liu and published by CRC Press. This book was released on 1999-01-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by applications to control theory and to the theory of partial differential equations (PDE's), the authors examine the exponential stability and analyticity of C0-semigroups associated with various dissipative systems. They present a unique, systematic approach in which they prove exponential stability by combining a theory from semigroup theory with partial differential equation techniques, and use an analogous theorem with PDE techniques to prove analyticity. The result is a powerful but simple tool useful in determining whether these properties will preserve for a given dissipative system. The authors show that the exponential stability is preserved for all the mechanical systems considered in this book-linear, one-dimensional thermoelastic, viscoelastic and thermoviscoelastic systems, plus systems with shear or friction damping. However, readers also learn that this property does not hold true for linear three-dimensional systems without making assumptions on the domain and initial data, and that analyticity is a more sensitive property, not preserved even for some of the systems addressed in this study.

Download or read book Semigroups Associated with Dissipative Systems written by Usa) Zhuangyi Liu (University of Minnesota and published by . This book was released on 1998-12-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Asymptotic Behavior of Dissipative Systems written by Jack K. Hale and published by American Mathematical Soc.. This book was released on 2010-01-04 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph reports the advances that have been made in the area by the author and many other mathematicians; it is an important source of ideas for the researchers interested in the subject. --Zentralblatt MATH Although advanced, this book is a very good introduction to the subject, and the reading of the abstract part, which is elegant, is pleasant. ... this monograph will be of valuable interest for those who aim to learn in the very rapidly growing subject of infinite-dimensional dissipative dynamical systems. --Mathematical Reviews This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor.

Download or read book Evolution Equations Semigroups and Functional Analysis written by Alfredo Lorenzi and published by Birkhäuser. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Evolution Equations Semigroups and Functional Analysis written by Brunello Terreni and published by Springer Science & Business Media. This book was released on 2002 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book A Short Course on Operator Semigroups written by Klaus-Jochen Engel and published by Springer Science & Business Media. This book was released on 2006-06-06 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.

Download or read book Nonlinear Parabolic Hyperbolic Coupled Systems and Their Attractors written by Yuming Qin and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent results concerning the global existence in time, the large-time behavior, decays of solutions and the existence of global attractors for nonlinear parabolic-hyperbolic coupled systems of evolutionary partial differential equations.

Download or read book Semigroup Theory with Applications to Systems and Control written by Nasir Uddin Ahmed and published by John Wiley & Sons. This book was released on 1991 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Global Well posedness and Asymptotic Behavior of the Solutions to Non classical Thermo visco elastic Models written by Yuming Qin and published by Springer. This book was released on 2016-07-29 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent findings on the global existence, the uniqueness and the large-time behavior of global solutions of thermo(vis)coelastic systems and related models arising in physics, mechanics and materials science such as thermoviscoelastic systems, thermoelastic systems of types II and III, as well as Timoshenko-type systems with past history. Part of the book is based on the research conducted by the authors and their collaborators in recent years. The book will benefit interested beginners in the field and experts alike.

Download or read book Positive Operator Semigroups written by András Bátkai and published by Birkhäuser. This book was released on 2017-02-13 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate the theory, like population equations, neutron transport theory, delay equations or flows in networks. Each chapter is accompanied by a large set of exercises. An up-to-date bibliography and a detailed subject index help the interested reader. The book is intended primarily for graduate and master students. The finite dimensional part, however, can be followed by an advanced bachelor with a solid knowledge of linear algebra and calculus.

Download or read book Analytic Inequalities and Their Applications in PDEs written by Yuming Qin and published by Birkhäuser. This book was released on 2017-02-13 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a number of analytic inequalities and their applications in partial differential equations. These include integral inequalities, differential inequalities and difference inequalities, which play a crucial role in establishing (uniform) bounds, global existence, large-time behavior, decay rates and blow-up of solutions to various classes of evolutionary differential equations. Summarizing results from a vast number of literature sources such as published papers, preprints and books, it categorizes inequalities in terms of their different properties.

Download or read book Research in PDEs and Related Fields written by Kaïs Ammari and published by Springer Nature. This book was released on 2022-11-07 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an accessible overview of mathematical control theory and analysis of PDEs, providing young researchers a snapshot of these active and rapidly developing areas. The chapters are based on two mini-courses and additional talks given at the spring school "Trends in PDEs and Related Fields” held at the University of Sidi Bel Abbès, Algeria from 8-10 April 2019. In addition to providing an in-depth summary of these two areas, chapters also highlight breakthroughs on more specific topics such as: Sobolev spaces and elliptic boundary value problems Local energy solutions of the nonlinear wave equation Geometric control of eigenfunctions of Schrödinger operators Research in PDEs and Related Fields will be a valuable resource to graduate students and more junior members of the research community interested in control theory and analysis of PDEs.

Download or read book Proceedings of the Third World Conference on Structural Control written by Fabio Casciati and published by John Wiley & Sons. This book was released on 2003-03-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Organized by the International Association for Structural Control(IASC), and sponsored by the European Association for the Controlof Structures (EACS), the recent world conference on structuralcontrol (3WCSC) brought together engineers, scientists, architects,builders and other practitioners interested in the general fieldsof active, hybrid and passive vibration control, health monitoringand damage detection, intelligent/smart materials and systems.Applications included buildings, bridges, space structures andcivil infrastructures under the action of dynamic environments(earthquake, wind, traffic...) and man-made loads. It provideda valuable forum for the discussion of the most pressing concernsin structural control and its related topics. The conference covered a wide range of topics including activeand semi-active control devices, passive control devices, controlalgorithms for linear and non-linear systems, modeling andidentification of structural systems, sensors, health monitoringand damage detection, benchmark test of building and bridges,innovative materials for structural control, applications toaerospace structures, applications to bridges, applications tocritical structures, external dynamic force characteristics andcontrollability issues, implications of severe ground motions, windforces, codes for structural control, and so forth. Suchcomprehensive treatment of the most innovative developments instructural control will make these volumes an informative referencefor all researchers and engineers interested in this area. Proceedings of the US - Europe Workshop On Sensors andSmart Structures Technology Como and Somma Lombardo, Italy In the last few years, significant progress has been made in thearea of sensing technology and structural healthmonitoring/condition assessment in the US and Europe. Innovativeconcepts involving new hardware, algorithms, and software have beenproposed. There have also been several full-scale trialimplementations of densely sensor-instrumented infrastructures andhealth monitoring systems, as well as case studies on bridges inEurope and in the US. Much can be learnt through US/European collaboration in the areaof experimental verification on small, medium, large and full-scaleprojects. Moreover, a common framework for expanded future jointresearch can be developed on the increased understanding achievedthrough mutual learning. This workshop consisted of seminar sessions on several themeswhich included innovative sensing hardware, advances in wirelesstechnology, and damage detection/characterization and conditionassessment methodologies. In addition, there were several workshopsessions devoted to summarizing the status of the sensors and smartstructures technologies in these topics, identifying the compellingresearch issues, and formulating an action plan withrecommendations for development and implementation through possiblecollaborative research projects and sharing of scientific data.

Download or read book Advanced Topics in Control Systems Theory written by Antonio Loría and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes selected contributions by lecturers at the third annual Formation d’Automatique de Paris. It provides a well-integrated synthesis of the latest thinking in nonlinear optimal control, observer design, stability analysis and structural properties of linear systems, without the need for an exhaustive literature review. The internationally known contributors to this volume represent many of the most reputable control centers in Europe.

Download or read book Boundary Synchronization for Hyperbolic Systems written by Tatsien Li and published by Springer Nature. This book was released on 2019-12-02 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within this carefully presented monograph, the authors extend the universal phenomenon of synchronization from finite-dimensional dynamical systems of ordinary differential equations (ODEs) to infinite-dimensional dynamical systems of partial differential equations (PDEs). By combining synchronization with controllability, they introduce the study of synchronization to the field of control and add new perspectives to the investigation of synchronization for systems of PDEs. With a focus on synchronization for a coupled system of wave equations, the text is divided into three parts corresponding to Dirichlet, Neumann, and coupled Robin boundary controls. Each part is then subdivided into chapters detailing exact boundary synchronization and approximate boundary synchronization, respectively. The core intention is to give artificial intervention to the evolution of state variables through appropriate boundary controls for realizing the synchronization in a finite time, creating a novel viewpoint into the investigation of synchronization for systems of partial differential equations, and revealing some essentially dissimilar characteristics from systems of ordinary differential equations. Primarily aimed at researchers and graduate students of applied mathematics and applied sciences, this text will particularly appeal to those interested in applied PDEs and control theory for distributed parameter systems.

Download or read book Control and Observer Design for Nonlinear Finite and Infinite Dimensional Systems written by Thomas Meurer and published by Springer Science & Business Media. This book was released on 2005-09-19 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents a well balanced combination of state-of-the-art theoretical results in the field of nonlinear controller and observer design, combined with industrial applications stemming from mechatronics, electrical, (bio–) chemical engineering, and fluid dynamics. The unique combination of results of finite as well as infinite–dimensional systems makes this book a remarkable contribution addressing postgraduates, researchers, and engineers both at universities and in industry. The contributions to this book were presented at the Symposium on Nonlinear Control and Observer Design: From Theory to Applications (SYNCOD), held September 15–16, 2005, at the University of Stuttgart, Germany. The conference and this book are dedicated to the 65th birthday of Prof. Dr.–Ing. Dr.h.c. Michael Zeitz to honor his life – long research and contributions on the fields of nonlinear control and observer design.

Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2009-04-29 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Differential Equations: Evolutionary Equations is the last text of a five-volume reference in mathematics and methodology. This volume follows the format set by the preceding volumes, presenting numerous contributions that reflect the nature of the area of evolutionary partial differential equations. The book is comprised of five chapters that feature the following: - A thorough discussion of the shallow-equations theory, which is used as a model for water waves in rivers, lakes and oceans. It covers the issues of modeling, analysis and applications - • Evaluation of the singular limits of reaction-diffusion systems, where the reaction is fast compared to the other processes; and applications that range from the theory of the evolution of certain biological processes to the phenomena of Turing and cross-diffusion instability - Detailed discussion of numerous problems arising from nonlinear optics, at the high-frequency and high-intensity regime • Geometric and diffractive optics, including wave interactions - Presentation of the issues of existence, blow-up and asymptotic stability of solutions, from the equations of solutions to the equations of linear and non-linear thermoelasticity - Answers to questions about unique space, such as continuation and backward uniqueness for linear second-order parabolic equations. Research mathematicians, mathematics lecturers and instructors, and academic students will find this book invaluable - Review of new results in the area - Continuation of previous volumes in the handbook series covering evolutionary PDEs - New content coverage of DE applications