| |
|
|
|
|
|
|
|
|
1. |
Record Nr. |
UNINA9910483440803321 |
|
|
Autore |
Xiao Ti-Jun <1964-> |
|
|
Titolo |
The Cauchy Problem for Higher Order Abstract Differential Equations / / by Ti-Jun Xiao, Jin Liang |
|
|
|
|
|
|
|
Pubbl/distr/stampa |
|
|
Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 1998 |
|
|
|
|
|
|
|
|
|
Edizione |
[1st ed. 1998.] |
|
|
|
|
|
Descrizione fisica |
|
1 online resource (XIV, 300 p.) |
|
|
|
|
|
|
Collana |
|
Lecture Notes in Mathematics, , 1617-9692 ; ; 1701 |
|
|
|
|
|
|
Disciplina |
|
|
|
|
|
|
Soggetti |
|
Differential equations |
Differential Equations |
|
|
|
|
|
|
|
|
Lingua di pubblicazione |
|
|
|
|
|
|
Formato |
Materiale a stampa |
|
|
|
|
|
Livello bibliografico |
Monografia |
|
|
|
|
|
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. |
|
|
|
|
|
| |