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|a 9783540494799
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|a 10.1007/978-3-540-49479-9
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|a Xiao, Ti-Jun.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a The Cauchy Problem for Higher Order Abstract Differential Equations
|h [electronic resource] /
|c by Ti-Jun Xiao, Jin Liang.
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|a 1st ed. 1998.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg :
|b Imprint: Springer,
|c 1998.
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|a XIV, 300 p.
|b online resource.
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|a text
|b txt
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1701
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|a 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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|a 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.
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|a Differential equations.
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|a Ordinary Differential Equations.
|0 http://scigraph.springernature.com/things/product-market-codes/M12147
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|a Liang, Jin.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783662178607
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|i Printed edition:
|z 9783540652380
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 1701
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|u https://doi.org/10.1007/978-3-540-49479-9
|z Full Text via HEAL-Link
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|a Mathematics and Statistics (Springer-11649)
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