04082nam 2200745 a 450 991081327530332120240516084837.01-283-39993-897866133999393-11-025027-610.1515/9783110250275(CKB)2550000000041596(EBL)736995(OCoLC)743693614(SSID)ssj0000530391(PQKBManifestationID)11364804(PQKBTitleCode)TC0000530391(PQKBWorkID)10576715(PQKB)10437925(MiAaPQ)EBC736995(DE-B1597)122836(OCoLC)753970239(OCoLC)755678913(DE-B1597)9783110250275(Au-PeEL)EBL736995(CaPaEBR)ebr10485452(CaONFJC)MIL339993(EXLCZ)99255000000004159620110303d2011 uy 0engur|n|---|||||txtccrPartial differential equations a unified Hilbert space approach /Rainer Picard, Des McGhee1st ed.Berlin ;New York De Gruyterc20111 online resource (488 p.)De Gruyter expositions in mathematics,0938-6572 ;55Description based upon print version of record.3-11-025026-8 Includes bibliographical references and index. Frontmatter -- Preface -- Contents -- Nomenclature -- Chapter 1 Elements of Hilbert Space Theory -- Chapter 2 Sobolev Lattices -- Chapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ∈ N -- Chapter 4 Linear Evolution Equations -- Chapter 5 Some Evolution Equations of Mathematical Physics -- Chapter 6 A "Royal Road" to Initial Boundary Value Problems of Mathematical Physics -- Conclusion -- Bibliography -- IndexThis book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.De Gruyter expositions in mathematics ;55.Hilbert spaceDifferential equations, PartialEvolution Equation.Hilbert Space.Mathematics.Partial Differential Equations.Sobolev.Hilbert space.Differential equations, Partial.515/.733SK 600rvkPicard R. H(Rainer H.)59385McGhee D. F59781MiAaPQMiAaPQMiAaPQBOOK9910813275303321Partial differential equations3993651UNINA