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.

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.

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

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.

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.

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.

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.

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.

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.

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.