The Cauchy problem for higher-order abstract differential equations /
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| Author / Creator: | Xiao, Ti-Jun, 1964- |
|---|---|
| Imprint: | Berlin ; New York : Springer, ©1998. |
| Description: | 1 online resource (xii, 300 pages). |
| Language: | English |
| Series: | Lecture notes in mathematics, 0075-8434 ; 1701 Lecture notes in mathematics (Springer-Verlag) ; 1701. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11065986 |
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| 100 | 1 | |a Xiao, Ti-Jun, |d 1964- |0 http://id.loc.gov/authorities/names/n98091504 |1 http://viaf.org/viaf/62381013 | |
| 245 | 1 | 4 | |a The Cauchy problem for higher-order abstract differential equations / |c Ti-Jun Xiao, Jin Liang. |
| 260 | |a Berlin ; |a New York : |b Springer, |c ©1998. | ||
| 300 | |a 1 online resource (xii, 300 pages). | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 490 | 1 | |a Lecture notes in mathematics, |x 0075-8434 ; |v 1701 | |
| 504 | |a Includes bibliographical references (pages 269-297) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |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. | |
| 520 | |a This monograph is the first systematic exposition of the theory of the Cauchy problem for higher order abstract linear differential equations, which covers all the main aspects of the developed theory. The main results are complete with detailed proofs and established recently, containing the corresponding theorems for first and incomplete second order cases and therefore for operator semigroups and cosine functions. They will find applications in many fields. The special power of treating the higher order problems directly is demonstrated, as well as that of the vector-valued Laplace transforms in dealing with operator differential equations and operator families. The reader is expected to have a knowledge of complex and functional analysis. | ||
| 650 | 0 | |a Differential equations. |0 http://id.loc.gov/authorities/subjects/sh85037890 | |
| 650 | 0 | |a Cauchy problem. |0 http://id.loc.gov/authorities/subjects/sh85021438 | |
| 650 | 0 | |a Banach spaces. |0 http://id.loc.gov/authorities/subjects/sh85011441 | |
| 650 | 0 | |a Hilbert space. |0 http://id.loc.gov/authorities/subjects/sh85060803 | |
| 650 | 7 | |a Banach spaces. |2 fast |0 (OCoLC)fst00826389 | |
| 650 | 7 | |a Cauchy problem. |2 fast |0 (OCoLC)fst00849796 | |
| 650 | 7 | |a Differential equations. |2 fast |0 (OCoLC)fst00893446 | |
| 650 | 7 | |a Hilbert space. |2 fast |0 (OCoLC)fst00956785 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Liang, Jin, |d 1964- |0 http://id.loc.gov/authorities/names/n98091507 |1 http://viaf.org/viaf/64679541 | |
| 776 | 0 | 8 | |i Print version: |a Xiao, Ti-Jun, 1964- |t Cauchy problem for higher-order abstract differential equations. |d Berlin ; New York : Springer, ©1998 |z 3540652388 |w (DLC) 98047648 |w (OCoLC)40163507 |
| 830 | 0 | |a Lecture notes in mathematics (Springer-Verlag) ; |v 1701. | |
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