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Hysteresis and Phase Transitions
Hysteresis is an exciting and mathematically challenging phenomenon that oc curs in rather different situations: jt, can be a byproduct offundamental physical mechanisms (such as phase transitions) or the consequence of a degradation or imperfection (like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hys teresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually non-smooth and thus not easy to treat mathematically. Hence it was only in the early seventies that the group of Russian scientists around M. A. Krasnoselskii initiated a systematic mathematical investigation of the phenomenon of hysteresis which culminated in the fundamental monograph Krasnoselskii-Pokrovskii (1983). In the meantime, many mathematicians have contributed to the mathematical theory, and the important monographs of 1. Mayergoyz (1991) and A. Visintin (1994a) have appeared. We came into contact with the notion of hysteresis around the year 1980.
Topics in Applied Analysis and Optimisation
This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
Optimal Control of Partial Differential Equations
The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.
Modelling and Control in Solid Mechanics
This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems is the availability of the inequality type constraints imposed on solutions such as the impenetration condition for contact problems, the yield plasticity condition, etc. As a consequence, the presence of free boundaries is typical of the boundary value problems concerned. The objective of the book is to display some new methods of analyzing such problems, as well as to perform research on new mode...
Differential Models of Hysteresis
Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis models, and illustrates several new results in this field.
Dissipative Phase Transitions
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. Content...
Control Theory of Partial Differential Equations
The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids a
IUTAM Symposium on Variations of Domain and Free-Boundary Problems in Solid Mechanics
Proceedings of the IUTAM Symposium held in Paris, France, 22-25 April 1997
Handbook of Differential Equations: Evolutionary Equations
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE’s, written by leading experts. - Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Control of Coupled Partial Differential Equations
This volume contains selected contributions originating from the ‘Conference on Optimal Control of Coupled Systems of Partial Differential Equations’, held at the ‘Mathematisches Forschungsinstitut Oberwolfach’ in April 2005. With their articles, leading scientists cover a broad range of topics such as controllability, feedback-control, optimality systems, model-reduction techniques, analysis and optimal control of flow problems, and fluid-structure interactions, as well as problems of shape and topology optimization. Applications affected by these findings are distributed over all time and length scales starting with optimization and control of quantum mechanical systems, the design of piezoelectric acoustic micro-mechanical devices, or optimal control of crystal growth to the control of bodies immersed into a fluid, airfoil design, and much more. The book addresses advanced students and researchers in optimization and control of infinite dimensional systems, typically represented by partial differential equations. Readers interested either in theory or in numerical simulation of such systems will find this book equally appealing.
