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001 978-3-030-00638-9
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008 181121s2018 gw | s |||| 0|eng d
020 _a9783030006389
_9978-3-030-00638-9
024 7 _a10.1007/978-3-030-00638-9
_2doi
040 _cCUS
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
082 0 4 _a515.7
_223
100 1 _aGie, Gung-Min.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSingular Perturbations and Boundary Layers
_h[electronic resource] /
_cby Gung-Min Gie, Makram Hamouda, Chang-Yeol Jung, Roger M. Temam.
250 _a1st ed. 2018.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2018.
300 _aXVIII, 412 p. 15 illus., 11 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 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v200
505 0 _aChapter 01- Singular perturbations in dimension one -- Chapter 2- Singular perturbations in higher dimensions in a channel -- Chapter 3- Boundary layers in a curved domain in Rd, d = 2;3 -- Chapter 4- Corner layers and turning points for convection-diffusion equations -- Chapter 5- Convection-diffusion equations in a circular domain with characteristic point layers -- Chapter 6- The Navier-Stokes equations in a periodic channel -- Chapter 7- The Navier-Stokes equations in a curved domain -- Appendix -- References.
520 _aSingular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.
650 0 _aFunctional analysis.
650 0 _aApproximation theory.
650 1 4 _aFunctional Analysis.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12066
650 2 4 _aApproximations and Expansions.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12023
700 1 _aHamouda, Makram.
700 1 _aJung, Chang-Yeol.
700 1 _aTemam, Roger M.
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v200
856 4 0 _uhttps://doi.org/10.1007/978-3-030-00638-9
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
942 _cEBK
999 _c206142
_d206142