The Cauchy problem for higher-order abstract differential equations / / Ti-Jun Xiao, Jin Liang

• Autore: Xiao Ti-Jun <1964->
• Pubblicazione: Berlin ; ; New York : , : Springer, , [1998]; ©1998
• Edizione: 1st ed. 1998.
• Descrizione fisica: 1 online resource (XIV, 300 p.)
• Disciplina: 515.35
• Soggetto topico: Differential equations; Cauchy problem; Banach spaces; Hilbert space
• Persona (resp. second.): LiangJin <1964->
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references (pages [269]-297) and index.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Cauchy problem for higher-order abstract differential equations
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910483440803321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture notes in mathematics (Springer-Verlag) ; ; 1701.