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Optimal Control of PDEs under Uncertainty, Jes?s Mart?nez-Frutos; Francisco Periago Esparza


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Автор: Jes?s Mart?nez-Frutos; Francisco Periago Esparza
Название:  Optimal Control of PDEs under Uncertainty
ISBN: 9783319982090
Издательство: Springer
Классификация:







ISBN-10: 3319982095
Обложка/Формат: Soft cover
Страницы: 123
Вес: 0.23 кг.
Дата издания: 2018
Серия: SpringerBriefs in Mathematics
Язык: English
Издание: 1st ed. 2018
Иллюстрации: 37 illustrations, color; 8 illustrations, black and white; xix, 123 p. 45 illus., 37 illus. in color.
Размер: 234 x 156 x 8
Читательская аудитория: Professional & vocational
Основная тема: Mathematics
Подзаголовок: An Introduction with Application to Optimal Shape Design of Structures
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This book provides a direct and comprehensive introduction to theoretical and numerical concepts in the emerging field of optimal control of partial differential equations (PDEs) under uncertainty. The main objective of the book is to offer graduate students and researchers a smooth transition from optimal control of deterministic PDEs to optimal control of random PDEs. Coverage includes uncertainty modelling in control problems, variational formulation of PDEs with random inputs, robust and risk-averse formulations of optimal control problems, existence theory and numerical resolution methods. The exposition focusses on the entire path, starting from uncertainty modelling and ending in the practical implementation of numerical schemes for the numerical approximation of the considered problems. To this end, a selected number of illustrative examples are analysed in detail throughout the book. Computer codes, written in MatLab, are provided for all these examples. This book is adressed to graduate students and researches in Engineering, Physics and Mathematics who are interested in optimal control and optimal design for random partial differential equations.
Дополнительное описание: 1 Introduction.- 2 Mathematical Preliminaires.- 3 Mathematical Analysis of Optimal Control Problems Under Uncertainty.- 4 Numerical Resolution of Robust Optimal Control Problems.- 5 Numerical Resolution of Risk Averse Optimal Control Problems.- 6 Structur


Nonlinear PDEs, Their Geometry, and Applications

Автор: Rados?aw A. Kycia; Maria U?an; Eivind Schneider
Название: Nonlinear PDEs, Their Geometry, and Applications
ISBN: 3030170306 ISBN-13(EAN): 9783030170301
Издательство: Springer
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Цена: 60550.00 T
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Описание:

This volume presents lectures given at the Summer School Wis?a 18: Nonlinear PDEs, Their Geometry, and Applications, which took place from August 20 - 30th, 2018 in Wis?a, Poland, and was organized by the Baltic Institute of Mathematics. The lectures in the first part of this volume were delivered by experts in nonlinear differential equations and their applications to physics. Original research articles from members of the school comprise the second part of this volume. Much of the latter half of the volume complements the methods expounded in the first half by illustrating additional applications of geometric theory of differential equations. Various subjects are covered, providing readers a glimpse of current research. Other topics covered include thermodynamics, meteorology, and the Monge–Amp?re equations.
Researchers interested in the applications of nonlinear differential equations to physics will find this volume particularly useful. A knowledge of differential geometry is recommended for the first portion of the book, as well as a familiarity with basic concepts in physics.

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

Автор: Pierluigi Colli; Angelo Favini; Elisabetta Rocca;
Название: Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
ISBN: 3319644882 ISBN-13(EAN): 9783319644882
Издательство: Springer
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Цена: 121110.00 T
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Описание: This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics.

Control of Wave and Beam PDEs

Автор: Bao-Zhu Guo; Jun-Min Wang
Название: Control of Wave and Beam PDEs
ISBN: 3030124800 ISBN-13(EAN): 9783030124809
Издательство: Springer
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Цена: 139750.00 T
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Описание: Control of Wave and Beam PDEs is a concise, self-contained introduction to Riesz bases in Hilbert space and their applications to control systems described by partial differential equations (PDEs). The authors discuss classes of systems that satisfy the spectral determined growth condition, the problem of stability, and the relationship between fulfillment of the condition and stability.Using the (fundamental) Riesz-basis property, the book shows how controllability, observability, stability, etc., can be derived for a linear system. The text provides a crash course in the mathematical theory of Riesz bases so that a reader can quickly understand this powerful method of dealing with linear PDEs. It introduces several important methods for achieving the Riesz basis property through spectral analysis, as well as new approaches including treatment of systems coupled through boundary weak connections.The book moves from a discussion of mathematical preliminaries through bases in Hilbert Spaces to applications to Euler–Bernoulli and Rayleigh beam equations and hybrid systems. The final chapter expands the use of the book’s methods to applications in other systems.Many typical examples, representing physical systems, are discussed in the text. The book is suitable not only for applied mathematicians seeking a powerful tool to understand control systems, but also for control engineers interested in the mathematics of PDE systems.

Formal Algorithmic Elimination for PDEs

Автор: Daniel Robertz
Название: Formal Algorithmic Elimination for PDEs
ISBN: 3319114441 ISBN-13(EAN): 9783319114446
Издательство: Springer
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Цена: 41920.00 T
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Описание:

Introduction.- Formal Methods for PDE Systems.- Differential Elimination for Analytic Functions.- Basic Principles and Supplementary Material.- References.- List of Algorithms.- List of Examples.- Index of Notation.- Index.


Adaptive Control of Hyperbolic PDEs

Автор: Henrik Anfinsen; Ole Morten Aamo
Название: Adaptive Control of Hyperbolic PDEs
ISBN: 3030058786 ISBN-13(EAN): 9783030058784
Издательство: Springer
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Цена: 93160.00 T
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Adaptive Control of Linear Hyperbolic PDEs provides a comprehensive treatment of adaptive control of linear hyperbolic systems, using the backstepping method. It develops adaptive control strategies for different combinations of measurements and actuators, as well as for a range of different combinations of parameter uncertainty. The book treats boundary control of systems of hyperbolic partial differential equations (PDEs) with uncertain parameters. The authors develop designs for single equations, as well as any number of coupled equations. The designs are accompanied by mathematical proofs, which allow the reader to gain insight into the technical challenges associated with adaptive control of hyperbolic PDEs, and to get an overview of problems that are still open for further research. Although stabilization of unstable systems by boundary control and boundary sensing are the particular focus, state-feedback designs are also presented. The book also includes simulation examples with implementational details and graphical displays, to give readers an insight into the performance of the proposed control algorithms, as well as the computational details involved. A library of MATLAB® code supplies ready-to-use implementations of the control and estimation algorithms developed in the book, allowing readers to tailor controllers for cases of their particular interest with little effort. These implementations can be used for many different applications, including pipe flows, traffic flow, electrical power lines, and more.Adaptive Control of Linear Hyperbolic PDEs is of value to researchers and practitioners in applied mathematics, engineering and physics; it contains a rich set of adaptive control designs, including mathematical proofs and simulation demonstrations. The book is also of interest to students looking to expand their knowledge of hyperbolic PDEs.

Recent Advances in PDEs: Analysis, Numerics and Control

Автор: Anna Doubova; Manuel Gonz?lez-Burgos; Francisco Gu
Название: Recent Advances in PDEs: Analysis, Numerics and Control
ISBN: 3319976125 ISBN-13(EAN): 9783319976129
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book contains the main results of the talks given at the workshop “Recent Advances in PDEs: Analysis, Numerics and Control”, which took place in Sevilla (Spain) on January 25-27, 2017. The work comprises 12 contributions given by high-level researchers in the partial differential equation (PDE) area to celebrate the 60th anniversary of Enrique Fern?ndez-Cara (University of Sevilla). The main topics covered here are: Control and inverse problems, Analysis of Fluid mechanics and Numerical Analysis. The work is devoted to researchers in these fields.

Geometry of pdes and related problems

Автор: Cabre, Xavier Henrot, Antoine Peralta-salas, Daniel Reichel, Wolfgang Shahgholian, Henrik
Название: Geometry of pdes and related problems
ISBN: 3319951858 ISBN-13(EAN): 9783319951850
Издательство: Springer
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Цена: 51230.00 T
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Описание: The aim of this book is to present different aspects of the deep interplay between Partial Differential Equations and Geometry. It gives an overview of some of the themes of recent research in the field and their mutual links, describing the main underlying ideas, and providing up-to-date references.Collecting together the lecture notes of the five mini-courses given at the CIME Summer School held in Cetraro (Cosenza, Italy) in the week of June 19–23, 2017, the volume presents a friendly introduction to a broad spectrum of up-to-date and hot topics in the study of PDEs, describing the state-of-the-art in the subject. It also gives further details on the main ideas of the proofs, their technical difficulties, and their possible extension to other contexts. Aiming to be a primary source for researchers in the field, the book will attract potential readers from several areas of mathematics.

Splines and PDEs: From Approximation Theory to Numerical Linear Algebra

Автор: Kunoth
Название: Splines and PDEs: From Approximation Theory to Numerical Linear Algebra
ISBN: 3319949101 ISBN-13(EAN): 9783319949109
Издательство: Springer
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Цена: 65210.00 T
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Описание: This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods.

Fully Nonlinear PDEs in Real and Complex Geometry and Optics

Автор: Luca Capogna; Pengfei Guan; Cristian E. Guti?rrez;
Название: Fully Nonlinear PDEs in Real and Complex Geometry and Optics
ISBN: 3319009419 ISBN-13(EAN): 9783319009414
Издательство: Springer
Рейтинг:
Цена: 32600.00 T
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Описание:

Introduction.- L∞ extremal mappings in AMLE and Teichmьller theory.- Curvature Measures, Isoperimetric Type Inequalities and Fully Nonlinear Pde's.- Refraction Problems In Geometric Optics.- On the Levi Monge-Ampиre equation.


Geometric methods in pde`s

Название: Geometric methods in pde`s
ISBN: 3319026658 ISBN-13(EAN): 9783319026657
Издательство: Springer
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Цена: 130430.00 T
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Описание: The analysis of PDEs is a prominent discipline in mathematics research, both in terms of its theoretical aspects and its relevance in applications. They describe a number of new achievements and/or the state of the art in their discipline of research, providing readers an overview of recent progress and future research trends in PDEs.

Numerical Methods for PDEs

Автор: Di Pietro
Название: Numerical Methods for PDEs
ISBN: 3319946757 ISBN-13(EAN): 9783319946757
Издательство: Springer
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Цена: 93160.00 T
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Описание: This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields.

Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications

Автор: Karl K. Sabelfeld, Irina A. Shalimova
Название: Spherical and Plane Integral Operators for PDEs: Construction, Analysis, and Applications
ISBN: 3110315297 ISBN-13(EAN): 9783110315295
Издательство: Walter de Gruyter
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Цена: 185890.00 T
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Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.


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