LEADER 04984nam 22007215 450 001 9910299994403321 005 20200630071521.0 010 $a3-319-10163-3 024 7 $a10.1007/978-3-319-10163-7 035 $a(CKB)3710000000244716 035 $a(EBL)1967975 035 $a(OCoLC)891584249 035 $a(SSID)ssj0001354341 035 $a(PQKBManifestationID)11705830 035 $a(PQKBTitleCode)TC0001354341 035 $a(PQKBWorkID)11327282 035 $a(PQKB)11575042 035 $a(MiAaPQ)EBC1967975 035 $a(DE-He213)978-3-319-10163-7 035 $a(PPN)181352419 035 $a(EXLCZ)993710000000244716 100 $a20140916d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aVariational Inequalities and Frictional Contact Problems$b[electronic resource] /$fby Anca Capatina 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (242 p.) 225 1 $aAdvances in Mechanics and Mathematics,$x1571-8689 ;$v31 300 $aDescription based upon print version of record. 311 $a3-319-10162-5 320 $aIncludes bibliographical references and index. 327 $aIntroduction -- Part I: Preliminaries -- Spaces of Real-valued Functions -- Spaces of Vector-valued Functions -- Part II: Variational Inequalities -- Existence and Uniqueness Results -- Some Properties of Solutions -- Dual Formulations -- Approximations of Variational Inequalities -- Part III: Contact Problems with Friction in Elasticity -- Static Problems -- Quasistatic Problems. 330 $aVariational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way. The readers will find a systematic and unified exposition on classical, variational and dual formulations, existence, uniqueness and regularity results, finite element approximations and related optimal control problems. This part of the book is an update of the Signorini problem with nonlocal Coulomb friction, a problem little studied and with few results in the literature. Also, in the quasi-static case, a control problem governed by a bilateral contact problem is studied. Despite the theoretical nature of the presented results, the book provides a background for the numerical analysis of contact problems. The materials presented are accessible to both graduate/under graduate students and to researchers in applied mathematics, mechanics, and engineering. The obtained results have numerous applications in mechanics, engineering and geophysics. The book contains a good amount of original results which, in this unified form, cannot be found anywhere else. 410 0$aAdvances in Mechanics and Mathematics,$x1571-8689 ;$v31 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aDifferential geometry 606 $aApplied mathematics 606 $aEngineering mathematics 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 606 $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022 606 $aMathematical and Computational Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T11006 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 0$aDifferential geometry. 615 0$aApplied mathematics. 615 0$aEngineering mathematics. 615 14$aManifolds and Cell Complexes (incl. Diff.Topology). 615 24$aDifferential Geometry. 615 24$aMathematical and Computational Engineering. 676 $a515.64 700 $aCapatina$b Anca$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721237 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299994403321 996 $aVariational inequalities and frictional contact problems$91409881 997 $aUNINA