01740nas 2200409 n 450 99000893995040332120240229084251.00379-56161020-2595000893995FED01000893995(Aleph)000893995FED01000893995CNRP 0023341820090724a19729999km-y0itaa50------bamulauu--------CIFA technical paper1972-RomeCommittee for Inland Fisheries of AfricaCommittee for Inland Fisheries of Africa technical paperDocument technique du CPCAFAO document technique du CPCACIFA technical paperCIFA TECH. PAP.341.1663FAO.Committee for Inland Fisheries of AfricaITACNP20090723http://acnp.cib.unibo.it/cgi-ser/start/it/cnr/dc-p1.tcl?catno=2276483&person=false&language=ITALIANO&libr=&libr_th=unina1Biblioteche che possiedono il periodicoSE990008939950403321Biblioteca Centralizzata. Facoltà di Agraria dell'Università Federico II di Napoli1978-1996;LAC.COLL. FAO 17FAGBCFAGBCCIFA technical paper796832UNINA866-01NA087 Biblioteca Centralizzata. Facoltà di Agraria dell'Università Federico II di Napoliv. Università, 100 Palazzo Reale, 80055 Portici (NA)081-2539322081-7760229itacnp.cib.unibo.itACNP Italian Union Catalogue of Serialshttp://acnp.cib.unibo.it/cgi-ser/start/it/cnr/df-p.tcl?catno=2276483&language=ITALIANO&libr=&person=&B=1&libr_th=unina&proposto=NO03749nam 22006735 450 991014629220332120250801064914.03-540-69594-X10.1007/BFb0092831(CKB)1000000000437343(SSID)ssj0000326692(PQKBManifestationID)12069599(PQKBTitleCode)TC0000326692(PQKBWorkID)10296698(PQKB)10963532(DE-He213)978-3-540-69594-3(MiAaPQ)EBC5577146(MiAaPQ)EBC6691771(Au-PeEL)EBL5577146(OCoLC)1066180869(Au-PeEL)EBL6691771(PPN)155195549(EXLCZ)99100000000043734320121227d1997 u| 0engurnn#008mamaatxtccrSobolev Gradients and Differential Equations /by john neuberger1st ed. 1997.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1997.1 online resource (VIII, 152 p.)Lecture Notes in Mathematics,1617-9692 ;1670Bibliographic Level Mode of Issuance: Monograph3-540-63537-8 Includes bibliographical references (pages [145]-149) and index.Several gradients -- Comparison of two gradients -- Continuous steepest descent in Hilbert space: Linear case -- Continuous steepest descent in Hilbert space: Nonlinear case -- Orthogonal projections, Adjoints and Laplacians -- Introducing boundary conditions -- Newton's method in the context of Sobolev gradients -- Finite difference setting: the inner product case -- Sobolev gradients for weak solutions: Function space case -- Sobolev gradients in non-inner product spaces: Introduction -- The superconductivity equations of Ginzburg-Landau -- Minimal surfaces -- Flow problems and non-inner product Sobolev spaces -- Foliations as a guide to boundary conditions -- Some related iterative methods for differential equations -- A related analytic iteration method -- Steepest descent for conservation equations -- A sample computer code with notes.A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.Lecture Notes in Mathematics,1617-9692 ;1670Differential equationsNumerical analysisDifferential EquationsNumerical AnalysisDifferential equations.Numerical analysis.Differential Equations.Numerical Analysis.515/.35365N30msc35A15mscNeuberger J. W(John W.),1934-61864MiAaPQMiAaPQMiAaPQBOOK9910146292203321Sobolev gradients and differential equations374787UNINA