03717nam 22006495 450 991029997690332120200706040331.03-0348-0736-810.1007/978-3-0348-0736-4(CKB)3710000000212205(Springer)9783034807364(MH)014131694-2(SSID)ssj0001296458(PQKBManifestationID)11721671(PQKBTitleCode)TC0001296458(PQKBWorkID)11347690(PQKB)11201961(DE-He213)978-3-0348-0736-4(MiAaPQ)EBC6314607(MiAaPQ)EBC5586448(Au-PeEL)EBL5586448(OCoLC)1066184980(PPN)179927000(EXLCZ)99371000000021220520140714d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierDispersive Equations and Nonlinear Waves Generalized Korteweg–de Vries, Nonlinear Schrödinger, Wave and Schrödinger Maps /by Herbert Koch, Daniel Tataru, Monica Vişan1st ed. 2014.Basel :Springer Basel :Imprint: Birkhäuser,2014.1 online resource (XII, 312 p. 1 illus.)online resourceOberwolfach Seminars,1661-237X ;45Bibliographic Level Mode of Issuance: Monograph3-0348-0735-X Includes bibliographical references (pages [309]-312).The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ideas and should provide graduate students with a stepping stone to this exciting direction of research.Oberwolfach Seminars,1661-237X ;45Partial differential equationsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Partial differential equations.Partial Differential Equations.515.355530.124Koch Herbertauthttp://id.loc.gov/vocabulary/relators/aut36792Tataru Danielauthttp://id.loc.gov/vocabulary/relators/autVişan Monicaauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299976903321Dispersive Equations and Nonlinear Waves2541504UNINAThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress