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AuthorXiao, Ti-Jun. author
TitleThe Cauchy Problem for Higher Order Abstract Differential Equations [electronic resource] / by Ti-Jun Xiao, Jin Liang
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1998
Connect tohttp://dx.doi.org/10.1007/978-3-540-49479-9
Descript XIV, 300 p. online resource

SUMMARY

The main purpose of this book is to present the basic theory and some recent deยญ 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 transยญ 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


CONTENT

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


Mathematics Differential equations Mathematics Ordinary Differential Equations



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