The Cauchy Problem for Higher Order Abstract Differential Equations

Jin Liang, Ti-Jun Xiao

ISBN 10: 3540652388 / ISBN 13: 9783540652380

Published by Springer Berlin Heidelberg, 1998

About this Item

Zustand: Gut - Gebrauchs- und Lagerspuren. Außen: verschmutzt. Innen: Seiten eingerissen. Aus der Auflösung einer renommierten Bibliothek. Kann Stempel beinhalten. | Seiten: 324 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 538545/203

Bibliographic Details

Title: The Cauchy Problem for Higher Order Abstract...

Publisher: Springer Berlin Heidelberg

Publication Date: 1998

Binding: Soft cover

Condition: Gut

About this title

Synopsis:

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.