Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
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Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
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Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. This first volume is devoted to domains whose boundary is smooth in the neighborhood of finitely many conical points. In particular, the theory encompasses the important case of domains with small holes. The second volume, on the other hand, treats perturbations of the boundary in higher dimensions as well as nonlocal perturbations. The core of this book consists of the solution of general elliptic boundary value problems by complete asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. The construction of this method capitalizes on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Much attention is paid to concrete problems in mathematical physics, for example in elasticity theory. In particular, a study of the asymptotic behavior of stress intensity factors, energy integrals and eigenvalues is presented. To a large extent the book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
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Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2000-05-01
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-01 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work is based on the authors' work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii
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Author : V. G. Mazʹi͡a︡
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii written by V. G. Mazʹi͡a︡ 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 2000 with Boundary value problems categories.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii
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Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2011-11-22
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-22 with Mathematics categories.
For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors’ work, and has no significant overlap with other books on the theory of elliptic boundary value problems
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
DOWNLOAD
Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2000-05-01
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-01 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, the second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this work are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the work is based on the authors' work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii
DOWNLOAD
Author : Vladimir Maz'ya
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains Volume Ii written by Vladimir Maz'ya and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For the first time in the mathematical literature this two-volume work introduces a unified and general approach to the asymptotic analysis of elliptic boundary value problems in singularly perturbed domains. While the first volume is devoted to perturbations of the boundary near isolated singular points, this second volume treats singularities of the boundary in higher dimensions as well as nonlocal perturbations. At the core of this book are solutions of elliptic boundary value problems by asymptotic expansion in powers of a small parameter that characterizes the perturbation of the domain. In particular, it treats the important special cases of thin domains, domains with small cavities, inclusions or ligaments, rounded corners and edges, and problems with rapid oscillations of the boundary or the coefficients of the differential operator. The methods presented here capitalize on the theory of elliptic boundary value problems with nonsmooth boundary that has been developed in the past thirty years. Moreover, a study on the homogenization of differential and difference equations on periodic grids and lattices is given. Much attention is paid to concrete problems in mathematical physics, particularly elasticity theory and electrostatics. To a large extent the book is based on the authors’ work and has no significant overlap with other books on the theory of elliptic boundary value problems.
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains
DOWNLOAD
Author : V. Maz'ya
language : en
Publisher:
Release Date : 2000
Asymptotic Theory Of Elliptic Boundary Value Problems In Singularly Perturbed Domains written by V. Maz'ya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Singularly Perturbed Boundary Value Problems
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Author : Matteo Dalla Riva
language : en
Publisher: Springer Nature
Release Date : 2021-10-01
Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.
This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains
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Author : Dmitrii Korikov
language : en
Publisher: Springer Nature
Release Date : 2021-04-01
Asymptotic Theory Of Dynamic Boundary Value Problems In Irregular Domains written by Dmitrii Korikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-01 with Mathematics categories.
This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.
Applications Of The Topological Derivative Method
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Author : Antonio André Novotny
language : en
Publisher: Springer
Release Date : 2018-12-28
Applications Of The Topological Derivative Method written by Antonio André Novotny and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-28 with Technology & Engineering categories.
The book presents new results and applications of the topological derivative method in control theory, topology optimization and inverse problems. It also introduces the theory in singularly perturbed geometrical domains using selected examples. Recognized as a robust numerical technique in engineering applications, such as topology optimization, inverse problems, imaging processing, multi-scale material design and mechanical modeling including damage and fracture evolution phenomena, the topological derivative method is based on the asymptotic approximations of solutions to elliptic boundary value problems combined with mathematical programming tools. The book presents the first order topology design algorithm and its applications in topology optimization, and introduces the second order Newton-type reconstruction algorithm based on higher order topological derivatives for solving inverse reconstruction problems. It is intended for researchers and students in applied mathematics and computational mechanics interested in the mathematical aspects of the topological derivative method as well as its applications in computational mechanics.