Karl Kunisch

Günter Leugering

Fredi Tröltzsch

Jürgen Sprekels

Contains contributions originating from the 'Conference on Optimal Control of Coupled Systems of Partial Differential Equations', held at the 'Mathematisches Forschungsinstitut Oberwolfach' in March 2008. This work covers a range of topics such as controllability, optimality systems, model-reduction techniques, and fluid-structure interactions.

Optimal Control of Coupled Systems of Partial Differential Equations

Dan Tiba

Dedicated to Prof. Dr. Fredi Tröltzsch on the Occasion of His 60th Birthday

Extensions of the Control Variational Method

Bernold Fiedler

Konrad Gröger

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences. Contents: Volume 1: Celestial MechanicsHomoclinic TangenciesSingular PerturbationsStochastic SystemsSymmetryTopological Methods and Conley IndexDelay EquationsGeometric DynamicsHyperbolic Conservation LawsHyperbolic Wave EquationsHysteresisLarge DomainsLattice Dynamical SystemsMicrostructureNonlinear Functional AnalysisVariational MethodsViscosity SolutionsGlobal Attractors and LimitsNonautonomous AttractorsOrder-Preserving Dynamical SystemsQualitative Theory of Parabolic EquationsStability of Fronts and Pulses Volume 2: Computer Algebra ToolsControl and OptimizationDynamics and AlgorithmsExponentially Small PhenomenaGeometric IntegratorsNumerical Ergodic TheoryNumerics of DynamicsChemistryChemotaxis, Cross-Diffusion, and Blow-UpIndustrial ApplicationsMechanicsModels in Biology, Medicine, and PhysiologyMolecular ModellingPatternsSemiconductorsSteady Water WavesUnsteady Hydrodynamic WavesDelay EquationsNumericsOrdinary Differential EquationsPartial Differential Equations Keywords:Dynamical Systems;Infinite Dimensions;Global Attractors;Stability;Computational Aspects;Celestial Mechanics;Homoclinic Tangencies;Singular Perturbations;Stochastic Systems;Conley Index;Delay Equations;Hyperbolic Wave Equations;Viscosity Solutions;Control and Optimization;Geometric Integrators;Numerical Ergodic Theory;Molecular Modelling;Patterns;Steady Water Waves

(In 2 Volumes)

Equadiff 99

Martin Brokate

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.

Hysteresis and Phase Transitions

Angelo Favini

Pierluigi Colli

Elisabetta Rocca

Giulio Schimperna

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.

In Honour of Prof. Gianni Gilardi

Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs

Jürgen Sprekels

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