LEADER 04082nam 2200745 a 450 001 9910813275303321 005 20240516084837.0 010 $a1-283-39993-8 010 $a9786613399939 010 $a3-11-025027-6 024 7 $a10.1515/9783110250275 035 $a(CKB)2550000000041596 035 $a(EBL)736995 035 $a(OCoLC)743693614 035 $a(SSID)ssj0000530391 035 $a(PQKBManifestationID)11364804 035 $a(PQKBTitleCode)TC0000530391 035 $a(PQKBWorkID)10576715 035 $a(PQKB)10437925 035 $a(MiAaPQ)EBC736995 035 $a(DE-B1597)122836 035 $a(OCoLC)753970239 035 $a(OCoLC)755678913 035 $a(DE-B1597)9783110250275 035 $a(Au-PeEL)EBL736995 035 $a(CaPaEBR)ebr10485452 035 $a(CaONFJC)MIL339993 035 $a(EXLCZ)992550000000041596 100 $a20110303d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aPartial differential equations $ea unified Hilbert space approach /$fRainer Picard, Des McGhee 205 $a1st ed. 210 $aBerlin ;$aNew York $cDe Gruyter$dc2011 215 $a1 online resource (488 p.) 225 1 $aDe Gruyter expositions in mathematics,$x0938-6572 ;$v55 300 $aDescription based upon print version of record. 311 $a3-11-025026-8 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $tNomenclature -- $tChapter 1 Elements of Hilbert Space Theory -- $tChapter 2 Sobolev Lattices -- $tChapter 3 Linear Partial Differential Equations with Constant Coefficients in Rn+1, n ? N -- $tChapter 4 Linear Evolution Equations -- $tChapter 5 Some Evolution Equations of Mathematical Physics -- $tChapter 6 A "Royal Road" to Initial Boundary Value Problems of Mathematical Physics -- $tConclusion -- $tBibliography -- $tIndex 330 $aThis book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics. 410 0$aDe Gruyter expositions in mathematics ;$v55. 606 $aHilbert space 606 $aDifferential equations, Partial 610 $aEvolution Equation. 610 $aHilbert Space. 610 $aMathematics. 610 $aPartial Differential Equations. 610 $aSobolev. 615 0$aHilbert space. 615 0$aDifferential equations, Partial. 676 $a515/.733 686 $aSK 600$2rvk 700 $aPicard$b R. H$g(Rainer H.)$059385 701 $aMcGhee$b D. F$059781 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813275303321 996 $aPartial differential equations$93993651 997 $aUNINA