The Cauchy Problem for Higher Order Abstract Differential Equations

1998
ISBN: 978-3-540-65238-0
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1701, 300 Seiten, Paperback, Format (B × H): 155 mm x 233 mm, Gewicht: 1010 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Liang, Jin

Xiao, Ti-Jun

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Geometrie
• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie

Inhaltsverzeichnis

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.