The Cauchy problem for higher-order abstract differential equations
Author(s)
Bibliographic Information
The Cauchy problem for higher-order abstract differential equations
（Lecture notes in mathematics, 1701）
Springer Verlag, c1998
Available at / 83 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||1701RM981219
-
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:515.3/X42070456695
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. [269]-297) and index
Description and Table of Contents
Description
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.
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.
by "Nielsen BookData"
