Moving Shape Analysis And Control

Problems involving the evolution of two- and three-dimensional domains arise in many areas of science and engineering. Emphasizing an Eulerian approach, Moving Shape Analysis and Control: Applications to Fluid Structure Interactions presents valuable tools for the mathematical analysis of evolving domains. The book illustrates the efficie

Addressing algebraic problems found in biomathematics and energy, Free and Moving Boundaries: Analysis, Simulation and Control discusses moving boundary and boundary control in systems described by partial differential equations (PDEs). With contributions from international experts, the book emphasizes numerical and theoretical control of moving boundaries in fluid structure couple systems, arteries, shape stabilization level methods, family of moving geometries, and boundary control. Using numerical analysis, the contributors examine the problems of optimal control theory applied to PDEs arising from continuum mechanics. The book presents several applications to electromagnetic devices, flow, control, computing, images analysis, topological changes, and free boundaries. It specifically focuses on the topics of boundary variation and control, dynamical control of geometry, optimization, free boundary problems, stabilization of structures, controlling fluid-structure devices, electromagnetism 3D, and inverse problems arising in areas such as biomathematics. Free and Moving Boundaries: Analysis, Simulation and Control explains why the boundary control of physical systems can be viewed as a moving boundary control, empowering the future research of select algebraic areas.

rd This book constitutes a collection of extended versions of papers presented at the 23 IFIP TC7 Conference on System Modeling and Optimization, which was held in C- cow, Poland, on July 23–27, 2007. It contains 7 plenary and 22 contributed articles, the latter selected via a peer reviewing process. Most of the papers are concerned with optimization and optimal control. Some of them deal with practical issues, e. g. , p- formance-based design for seismic risk reduction, or evolutionary optimization in structural engineering. Many contributions concern optimization of infini- dimensional systems, ranging from a general overview of the variational analysis, through optimization and sensitivity analysis of PDE systems, to optimal control of neutral systems. A significant group of papers is devoted to shape analysis and opti- zation. Sufficient optimality conditions for ODE problems, and stochastic control methods applied to mathematical finance, are also investigated. The remaining papers are on mathematical programming, modeling, and information technology. The conference was the 23rd event in the series of such meetings biennially org- ized under the auspices of the Seventh Technical Committee “Systems Modeling and Optimization” of the International Federation for Information Processing (IFIP TC7).

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.

This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied mathematics, physics, seismology, engineering, and industry with an extensive knowledge of mathematical analysis, it helps readers understand how mathematical theory can be applied to various phenomena, and conversely, how to formulate actual phenomena as mathematical problems. This book is the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS) 15 and CoMFoS16.

The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics. Contents:Dirichlet Problems with Mean Curvature Operator in Minkowski Space (Cristian Bereanu, Petru Jebelean and Călin Şerban)Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis (Lorena Bociu and Kristina Martin)Non-Smooth Regularization of a Forward-Backward Parabolic Equation (Elena Bonetti, Pierluigi Colli and Giuseppe Tomassetti)Approaching Monotone Inclusion Problems via Second Order Dynamical Systems with Linear and Anisotropic Damping (Radu Ioan Boţ and Ernö Robert Csetnek)On the Solutions of a Quadratic Integral Inclusion (Aurelian Cernea)On the Bounded and Stabilizing Solution of a Generalized Riccati Differential Equation with Periodic Coefficients Arising in Connection with a Zero Sum Linear Quadratic Stochastic Differential Game (Vasile Dragan and Toader Morozan)A Maximum Principle for a Class of First Order Differential Operators (Maria Fărcăşeanu, Mihai Mihăilescu and Denisa Stancu-Dumitru)Differentiability and Integrability Properties for Solutions to Nonlocal Equations (Mikil Foss and Petronela Radu)Ferroelectric Thin Structures (Antonio Gaudiello and Kamel Hamdache)Sliding Modes for a Phase-Field System (Gianni Gilardi)Uniformly Hyperbolic Viable Sets in Affine IFS (Vasile Glavan and Valeriu Guţu)Some Support Considerations in the Asymptotic Optimality of Two-Scale Controlled PDMP (Dan Goreac and Oana Silvia Serea)Inverse Problems for Control Theory (Mohammed Al Horani and Angelo Favini)On the Ill-Posedness of Active Scalar Equations with Odd Singular Kernels (Igor Kukavica, Vlad Vicol and Fei Wang)Equilibrium in an Individual — Societal SIR Vaccination Model in Presence of Discounting and Finite Vaccination Capacity (Laetitia Laguzet, Gabriel Turinici and Ghozlane Yahiaoui)On Some Minimization Problems in RN (Mihai Mariş)Recent Results on Multiple Periodic Solutions of Forced Relativistic Pendulum-Type Continuous and Discrete Systems (Jean Mawhin)On the Anisotropic Caginalp Phase-Field System with Singular Nonlinear Terms (Alain Miranville)Space, Time, Similarity (Umberto Mosco)Singularly Perturbed Problems for Abstract Differential Equations of Second Order in Hilbert Spaces (Andrei Perjan and Galina Rusu)Global Controllability and Mixing for the Burgers Equation with Localised Finite-Dimensional External Force (Armen Shirikyan)Boundary Observation in Shape Optimization (Dan Tiba)Recent Progress on Steady Gravity Water Waves (Eugen Vărvărucă) Readership: Researchers in partial differential equations, calculus of variations and optimal control, difference and functional equations.

Presents Real & Complex Analysis Together Using a Unified Approach A two-semester course in analysis at the advanced undergraduate or first-year graduate level Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA’s 2004 Curriculum Guide. By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of analysis right from the beginning. This combined development also allows for a more streamlined approach to real and complex function theory. Enhanced by more than 1,000 exercises, the text covers all the essential topics usually found in separate treatments of real analysis and complex analysis. Ancillary materials are available on the book’s website. This book offers a unique, comprehensive presentation of both real and complex analysis. Consequently, students will no longer have to use two separate textbooks—one for real function theory and one for complex function theory.

Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.