Existence And Regularity Results For Some Shape Optimization Problems
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Existence And Regularity Results For Some Shape Optimization Problems
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Author : Bozhidar Velichkov
language : en
Publisher: Springer
Release Date : 2015-03-21
Existence And Regularity Results For Some Shape Optimization Problems written by Bozhidar Velichkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-21 with Mathematics categories.
We study the existence and regularity of optimal domains for functionals depending on the spectrum of the Dirichlet Laplacian or of more general Schrödinger operators. The domains are subject to perimeter and volume constraints; we also take into account the possible presence of geometric obstacles. We investigate the properties of the optimal sets and of the optimal state functions. In particular, we prove that the eigenfunctions are Lipschitz continuous up to the boundary and that the optimal sets subject to the perimeter constraint have regular free boundary. We also consider spectral optimization problems in non-Euclidean settings and optimization problems for potentials and measures, as well as multiphase and optimal partition problems.
Variational Methods In Shape Optimization Problems
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Author : Dorin Bucur
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-13
Variational Methods In Shape Optimization Problems written by Dorin Bucur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-13 with Mathematics categories.
Shape optimization problems are treated from the classical and modern perspectives Targets a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical problems Requires only a standard knowledge in the calculus of variations, differential equations, and functional analysis Driven by several good examples and illustrations Poses some open questions.
New Trends In Shape Optimization
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Author : Aldo Pratelli
language : en
Publisher: Birkhäuser
Release Date : 2015-12-01
New Trends In Shape Optimization written by Aldo Pratelli and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-01 with Mathematics categories.
This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.
Introduction To Shape Optimization
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Author : J. Haslinger
language : en
Publisher: SIAM
Release Date : 2003-01-01
Introduction To Shape Optimization written by J. Haslinger and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization comprehensively, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Applications include contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics. Audience: the book is written primarily for students of applied mathematics, scientific computing, and mechanics. Most of the material is directed toward graduate students, although a portion of it is suitable for senior undergraduate students. Readers are assumed to have some knowledge of partial differential equations and their numerical solution, as well as modern programming language such as C++ Fortran 90.
Shape Optimization Problems
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Author : Hideyuki Azegami
language : en
Publisher: Springer Nature
Release Date : 2020-09-30
Shape Optimization Problems written by Hideyuki Azegami and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-30 with Mathematics categories.
This book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations. The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Regularity Of The One Phase Free Boundaries
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Author : Bozhidar Velichkov
language : en
Publisher: Springer Nature
Release Date : 2023-02-24
Regularity Of The One Phase Free Boundaries written by Bozhidar Velichkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-24 with Mathematics categories.
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research. The exposition is organized around four main theorems, which are dedicated to the one-phase functional in its simplest form. Many of the methods and the techniques presented here are very recent and were developed in the context of different free boundary problems. We also give the detailed proofs of several classical results, which are based on some universal ideas and are recurrent in the free boundary, PDE and the geometric regularity theories. This book is aimed at graduate students and researches and is accessible to anyone with a moderate level of knowledge of elliptical PDEs.
Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations
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Author : Maria Colombo
language : en
Publisher: Springer
Release Date : 2017-06-07
Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations written by Maria Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with Mathematics categories.
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Rigid Germs The Valuative Tree And Applications To Kato Varieties
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Author : Matteo Ruggiero
language : en
Publisher: Springer
Release Date : 2016-04-28
Rigid Germs The Valuative Tree And Applications To Kato Varieties written by Matteo Ruggiero and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Mathematics categories.
This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds. The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates. In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.
Recent Advances In Partial Differential Equations And Applications
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Author : Vicenţiu D. Rădulescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-28
Recent Advances In Partial Differential Equations And Applications written by Vicenţiu D. Rădulescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Differential equations, Partial categories.
This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.
Shape Optimization And Optimal Design
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Author : John Cagnol
language : en
Publisher: CRC Press
Release Date : 2017-08-02
Shape Optimization And Optimal Design written by John Cagnol and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-02 with Mathematics categories.
This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.