The Resource Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves
Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves
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The item Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green's function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green's functions and solutions of boundary value problems for mesoscale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green's kernels in domains with singularly perturbed boundaries and (b) mesoscale asymptotic approximations of physical fields in nonperiodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables. This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations
 Language
 eng
 Extent
 1 online resource (xvii, 258 pages)
 Contents

 Green's Tensor in Bodies with Multiple Rigid Inclusions
 Green's Tensor for the Mixed Boundary Value Problem in a Domain with a Small Hole
 Mesoscale Approximations: Asymptotic Treatment of Perforated Domains Without Homogenization.
 Mesoscale Approximations for Solutions of Dirichlet Problems
 Mixed Boundary Value Problems in MultiplyPerforated Domains
 Green's Functions in Singularly Perturbed Domains.
 Uniform Asymptotic Formulae for Green's Functions for the Laplacian in Domains with Small Perforations
 Mixed and Neumann Boundary Conditions for Domains with Small Holes and Inclusions: Uniform Asymptotics of Green's Kernels
 Green's Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions
 Numerical Simulations Based on the Asymptotic Approximations
 Other Examples of Asymptotic Approximations of Green's Functions in Singularly Perturbed Domains
 Green's Tensors for Vector Elasticity in Bodies with Small Defects.
 Green's Tensor for the Dirichlet Boundary Value Problem in a Domain with a Single Inclusion
 Isbn
 9783319003573
 Label
 Green's kernels and mesoscale approximations in perforated domains
 Title
 Green's kernels and mesoscale approximations in perforated domains
 Statement of responsibility
 Vladimir Maz'ya, Alexander Movchan, Michael Nieves
 Subject

 Approximation theory
 Approximation theory
 Approximations and Expansions.
 Boundary value problems
 Boundary value problems
 Boundary value problems
 Boundary value problems  Asymptotic theory
 Boundary value problems  Asymptotic theory
 Boundary value problems  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, partial.
 Green's functions
 Green's functions
 Green's functions
 Inhomogeneous materials  Mathematical models
 Inhomogeneous materials  Mathematical models
 Inhomogeneous materials  Mathematical models
 Mathematics.
 Partial Differential Equations.
 Approximation theory
 Language
 eng
 Summary
 There are a wide range of applications in physics and structural mechanics involving domains with singular perturbations of the boundary. Examples include perforated domains and bodies with defects of different types. The accurate direct numerical treatment of such problems remains a challenge. Asymptotic approximations offer an alternative, efficient solution. Green's function is considered here as the main object of study rather than a tool for generating solutions of specific boundary value problems. The uniformity of the asymptotic approximations is the principal point of attention. We also show substantial links between Green's functions and solutions of boundary value problems for mesoscale structures. Such systems involve a large number of small inclusions, so that a small parameter, the relative size of an inclusion, may compete with a large parameter, represented as an overall number of inclusions. The main focus of the present text is on two topics: (a) asymptotics of Green's kernels in domains with singularly perturbed boundaries and (b) mesoscale asymptotic approximations of physical fields in nonperiodic domains with many inclusions. The novel feature of these asymptotic approximations is their uniformity with respect to the independent variables. This book addresses the needs of mathematicians, physicists and engineers, as well as research students interested in asymptotic analysis and numerical computations for solutions to partial differential equations
 Cataloging source
 GW5XE
 http://library.link/vocab/creatorName
 Mazʹi︠a︡, V. G
 Dewey number
 515/.22
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA331
 LC item number
 .M39 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName

 Movchan, A. B.
 Nieves, Michael
 Series statement
 Lecture notes in mathematics,
 Series volume
 2077
 http://library.link/vocab/subjectName

 Green's functions
 Differential equations, Elliptic
 Boundary value problems
 Inhomogeneous materials
 Boundary value problems
 Approximation theory
 Approximation theory
 Boundary value problems
 Boundary value problems
 Differential equations, Elliptic
 Green's functions
 Inhomogeneous materials
 Label
 Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 251253) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Green's Tensor in Bodies with Multiple Rigid Inclusions
 Green's Tensor for the Mixed Boundary Value Problem in a Domain with a Small Hole
 Mesoscale Approximations: Asymptotic Treatment of Perforated Domains Without Homogenization.
 Mesoscale Approximations for Solutions of Dirichlet Problems
 Mixed Boundary Value Problems in MultiplyPerforated Domains
 Green's Functions in Singularly Perturbed Domains.
 Uniform Asymptotic Formulae for Green's Functions for the Laplacian in Domains with Small Perforations
 Mixed and Neumann Boundary Conditions for Domains with Small Holes and Inclusions: Uniform Asymptotics of Green's Kernels
 Green's Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions
 Numerical Simulations Based on the Asymptotic Approximations
 Other Examples of Asymptotic Approximations of Green's Functions in Singularly Perturbed Domains
 Green's Tensors for Vector Elasticity in Bodies with Small Defects.
 Green's Tensor for the Dirichlet Boundary Value Problem in a Domain with a Single Inclusion
 Control code
 849509026
 Dimensions
 unknown
 Extent
 1 online resource (xvii, 258 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319003573
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319003573
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)849509026
 Label
 Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 251253) and indexes
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 Green's Tensor in Bodies with Multiple Rigid Inclusions
 Green's Tensor for the Mixed Boundary Value Problem in a Domain with a Small Hole
 Mesoscale Approximations: Asymptotic Treatment of Perforated Domains Without Homogenization.
 Mesoscale Approximations for Solutions of Dirichlet Problems
 Mixed Boundary Value Problems in MultiplyPerforated Domains
 Green's Functions in Singularly Perturbed Domains.
 Uniform Asymptotic Formulae for Green's Functions for the Laplacian in Domains with Small Perforations
 Mixed and Neumann Boundary Conditions for Domains with Small Holes and Inclusions: Uniform Asymptotics of Green's Kernels
 Green's Function for the Dirichlet Boundary Value Problem in a Domain with Several Inclusions
 Numerical Simulations Based on the Asymptotic Approximations
 Other Examples of Asymptotic Approximations of Green's Functions in Singularly Perturbed Domains
 Green's Tensors for Vector Elasticity in Bodies with Small Defects.
 Green's Tensor for the Dirichlet Boundary Value Problem in a Domain with a Single Inclusion
 Control code
 849509026
 Dimensions
 unknown
 Extent
 1 online resource (xvii, 258 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9783319003573
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319003573
 Other physical details
 illustrations.
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)849509026
Subject
 Approximation theory
 Approximation theory
 Approximations and Expansions.
 Boundary value problems
 Boundary value problems
 Boundary value problems
 Boundary value problems  Asymptotic theory
 Boundary value problems  Asymptotic theory
 Boundary value problems  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, Elliptic  Asymptotic theory
 Differential equations, partial.
 Green's functions
 Green's functions
 Green's functions
 Inhomogeneous materials  Mathematical models
 Inhomogeneous materials  Mathematical models
 Inhomogeneous materials  Mathematical models
 Mathematics.
 Partial Differential Equations.
 Approximation theory
Member of
 Lecture notes in mathematics (SpringerVerlag), 2077
 Lecture notes in mathematics (SpringerVerlag), 2077.
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Greenskernelsandmesoscaleapproximationsin/NQXAdJPDGE/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Greenskernelsandmesoscaleapproximationsin/NQXAdJPDGE/">Green's kernels and mesoscale approximations in perforated domains, Vladimir Maz'ya, Alexander Movchan, Michael Nieves</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>