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

By Ti-Jun Xiao and Jin Liang

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.

• Format: Paperback
• Language: English
• ISBN: 3540652388
• ISBN13: 9783540652380
• Release Date: May 1999
• Publisher: Springer
• Length: 300 Pages
• Weight: 1.00 lbs.
• Dimensions: 0.7" x 6.1" x 9.2"