000 03413nam a22004695i 4500
001 978-3-540-49479-9
003 DE-He213
005 20190213151900.0
007 cr nn 008mamaa
008 131201s1998 gw | s |||| 0|eng d
020 _a9783540494799
_9978-3-540-49479-9
024 7 _a10.1007/978-3-540-49479-9
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aXiao, Ti-Jun.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 4 _aThe Cauchy Problem for Higher Order Abstract Differential Equations
_h[electronic resource] /
_cby Ti-Jun Xiao, Jin Liang.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1998.
300 _aXIV, 300 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1701
505 0 _aLaplace 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.
520 _aThe 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.
650 0 _aDifferential Equations.
650 1 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
700 1 _aLiang, Jin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783662178607
776 0 8 _iPrinted edition:
_z9783540652380
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1701
856 4 0 _uhttps://doi.org/10.1007/978-3-540-49479-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
912 _aZDB-2-BAE
999 _c12209
_d12209