The Cauchy Problem for Higher Order Abstract Differential Equations

• Main Authors: Xiao, Ti-Jun (Author, http://id.loc.gov/vocabulary/relators/aut), Liang, Jin (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998.
• Edition: 1st ed. 1998.
• Series: Lecture Notes in Mathematics, 1701
• Subjects: Differential equations.; Ordinary Differential Equations.

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 vec...

Table of Contents:

• 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.