LEADER 03634nam 22006135 450 001 9910483440803321 005 20250731082234.0 024 7 $a10.1007/978-3-540-49479-9 035 $a(CKB)2560000000154829 035 $a(SSID)ssj0000492312 035 $a(PQKBManifestationID)11338589 035 $a(PQKBTitleCode)TC0000492312 035 $a(PQKBWorkID)10478619 035 $a(PQKB)11144357 035 $a(DE-He213)978-3-540-49479-9 035 $a(MiAaPQ)EBC5591384 035 $a(MiAaPQ)EBC6711216 035 $a(Au-PeEL)EBL5591384 035 $a(OCoLC)1066196211 035 $a(Au-PeEL)EBL6711216 035 $a(OCoLC)1272996068 035 $a(PPN)238069109 035 $a(EXLCZ)992560000000154829 100 $a20131201d1998 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Cauchy Problem for Higher Order Abstract Differential Equations /$fby Ti-Jun Xiao, Jin Liang 205 $a1st ed. 1998. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1998. 215 $a1 online resource (XIV, 300 p.) 225 1 $aLecture Notes in Mathematics,$x1617-9692 ;$v1701 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$aPrinted edition: 9783540652380 320 $aIncludes bibliographical references (pages [269]-297) and index. 327 $aLaplace transforms and operator families in locally convex spaces -- Wellposedness and solvability -- Generalized wellposedness -- Analyticity and parabolicity -- Exponential growth bound and exponential stability -- Differentiability and norm continuity -- Almost periodicity -- Appendices: A1 Fractional powers of non-negative operators -- A2 Strongly continuous semigroups and cosine functions -- Bibliography -- Index -- Symbols. 330 $aThe main purpose of this book is to present the basic theory and some recent de­ velopments concerning the Cauchy problem for higher order abstract differential equations u(n)(t) + ~ AiU(i)(t) = 0, t ~ 0, { U(k)(O) = Uk, 0 ~ k ~ n-l. where AQ, Ab . . . , A - are linear operators in a topological vector space E. n 1 Many problems in nature can be modeled as (ACP ). For example, many n initial value or initial-boundary value problems for partial differential equations, stemmed from mechanics, physics, engineering, control theory, etc. , can be trans­ lated into this form by regarding the partial differential operators in the space variables as operators Ai (0 ~ i ~ n - 1) in some function space E and letting the boundary conditions (if any) be absorbed into the definition of the space E or of the domain of Ai (this idea of treating initial value or initial-boundary value problems was discovered independently by E. Hille and K. Yosida in the forties). The theory of (ACP ) is closely connected with many other branches of n mathematics. Therefore, the study of (ACPn) is important for both theoretical investigations and practical applications. Over the past half a century, (ACP ) has been studied extensively. 410 0$aLecture Notes in Mathematics,$x1617-9692 ;$v1701 606 $aDifferential equations 606 $aDifferential Equations 615 0$aDifferential equations. 615 14$aDifferential Equations. 676 $a515.35 700 $aXiao$b Ti-Jun$f1964-$062026 702 $aLiang$b Jin$f1964- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483440803321 996 $aCauchy problem for higher-order abstract differential equations$91502020 997 $aUNINA