The Cauchy problem for higher-order abstract differential equations
著者
書誌事項
The Cauchy problem for higher-order abstract differential equations
（Lecture notes in mathematics, 1701）
Springer Verlag, c1998
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注記
Includes bibliographical references (p. [269]-297) and index
内容説明・目次
内容説明
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.
目次
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.
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