The Cauchy Problem for Higher Order Abstract Differential Equations (Lecture Notes in Mathematics)

Jin Liang, Ti-Jun Xiao

ISBN 10: 3540652388 / ISBN 13: 9783540652380

Published by Springer 2008-06-13, 2008

About this Item

Seller Inventory # 6666-IUK-9783540652380

Bibliographic Details

• Title: The Cauchy Problem for Higher Order Abstract Differential Equations (Lecture Notes in Mathematics)
• Publisher: Springer 2008-06-13
• Publication Date: 2008
• Language: English
• ISBN 10: 3540652388
• ISBN 13: 9783540652380
• Binding: Paperback
• Condition: New

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.