000 04665nam a22004935i 4500
001 978-3-319-00357-3
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008 130607s2013 gw | s |||| 0|eng d
020 _a9783319003573
_9978-3-319-00357-3
024 7 _a10.1007/978-3-319-00357-3
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.353
_223
100 1 _aMaz'ya, Vladimir.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aGreen's Kernels and Meso-Scale Approximations in Perforated Domains
_h[electronic resource] /
_cby Vladimir Maz'ya, Alexander Movchan, Michael Nieves.
264 1 _aHeidelberg :
_bSpringer International Publishing :
_bImprint: Springer,
_c2013.
300 _aXVII, 258 p. 17 illus., 10 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2077
505 0 _aPart I: 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 -- Part II: 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 -- 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 -- Part III Meso-scale approximations. Asymptotic treatment of perforated domains without homogenization: Meso-scale approximations for solutions of Dirichlet problems -- Mixed boundary value problems in multiply-perforated domains.
520 _aThere 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 meso-scale 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) meso-scale asymptotic approximations of physical fields in non-periodic 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.
650 0 _aDifferential equations, partial.
650 0 _aMathematics.
650 1 4 _aPartial Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12155
650 2 4 _aApproximations and Expansions.
_0http://scigraph.springernature.com/things/product-market-codes/M12023
700 1 _aMovchan, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
700 1 _aNieves, Michael.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319003566
776 0 8 _iPrinted edition:
_z9783319003580
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2077
856 4 0 _uhttps://doi.org/10.1007/978-3-319-00357-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c9338
_d9338