03634nam 22006135 450 991048344080332120250731082234.010.1007/978-3-540-49479-9(CKB)2560000000154829(SSID)ssj0000492312(PQKBManifestationID)11338589(PQKBTitleCode)TC0000492312(PQKBWorkID)10478619(PQKB)11144357(DE-He213)978-3-540-49479-9(MiAaPQ)EBC5591384(MiAaPQ)EBC6711216(Au-PeEL)EBL5591384(OCoLC)1066196211(Au-PeEL)EBL6711216(OCoLC)1272996068(PPN)238069109(EXLCZ)99256000000015482920131201d1998 u| 0engurnn|008mamaatxtccrThe Cauchy Problem for Higher Order Abstract Differential Equations /by Ti-Jun Xiao, Jin Liang1st ed. 1998.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,1998.1 online resource (XIV, 300 p.) Lecture Notes in Mathematics,1617-9692 ;1701Bibliographic Level Mode of Issuance: MonographPrinted edition: 9783540652380 Includes bibliographical references (pages [269]-297) and index.Laplace 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.The 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.Lecture Notes in Mathematics,1617-9692 ;1701Differential equationsDifferential EquationsDifferential equations.Differential Equations.515.35Xiao Ti-Jun1964-62026Liang Jin1964-MiAaPQMiAaPQMiAaPQBOOK9910483440803321Cauchy problem for higher-order abstract differential equations1502020UNINA