LEADER 03719nam 2200673 450 001 996466499703316 005 20220513024102.0 024 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 $a20220513d1998 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 14$aThe Cauchy problem for higher-order abstract differential equations /$fTi-Jun Xiao, Jin Liang 205 $a1st ed. 1998. 210 1$aBerlin ;$aNew York :$cSpringer,$d[1998] 210 4$dİ1998 215 $a1 online resource (XIV, 300 p.) 225 1 $aLecture notes in mathematics ;$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 (Springer-Verlag) ;$v1701. 606 $aDifferential equations 606 $aCauchy problem 606 $aBanach spaces 606 $aHilbert space 615 0$aDifferential equations. 615 0$aCauchy problem. 615 0$aBanach spaces. 615 0$aHilbert space. 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 $a996466499703316 996 $aCauchy problem for higher-order abstract differential equations$91502020 997 $aUNISA