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Titlebook: Semigroups of Linear Operators and Applications to Partial Differential Equations; A. Pazy Book 1983 Springer-Verlag New York, Inc. 1983 A

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书目名称Semigroups of Linear Operators and Applications to Partial Differential Equations
编辑A. Pazy
视频video
丛书名称Applied Mathematical Sciences
图书封面Titlebook: Semigroups of Linear Operators and Applications to Partial Differential Equations;  A. Pazy Book 1983 Springer-Verlag New York, Inc. 1983 A
描述.From the reviews.: "Since E. Hille and K. Yoshida established the characterization of generators of .C.0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about .C.0 semigroups." #.Bulletin Applied Mathematical Sciences 4/85.#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy‘s decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one
出版日期Book 1983
关键词Anfangswertproblem; Applications; Equations; Operatorhalbgruppe; Operators; Partielle Differentialgleichu
版次1
doihttps://doi.org/10.1007/978-1-4612-5561-1
isbn_softcover978-1-4612-5563-5
isbn_ebook978-1-4612-5561-1Series ISSN 0066-5452 Series E-ISSN 2196-968X
issn_series 0066-5452
copyrightSpringer-Verlag New York, Inc. 1983
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Spectral Properties and Regularity,nsider now the operator . where . — lim denotes the weak limit in .. The domain of . is the set of all x ϵ. forr which the weak limit on the right-hand side of (1.1) exists. Since the existence of a limit implies the existence of a weak limit, it is clear that à extends .. That this extension is not
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,Applications to Partial Differential Equations—Nonlinear Equations,uation in ∝. . where . is a complex valued function and . a real constant. The space in which this problem will be considered is L.(R.). Defining the linear operator . by .(R.)and . = — . & . for . ϵ .(.) the initial value problem (1.1) can be rewritten as .where ..
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Evolution Equations,Let . be a Banach space. For every .,0 ≤. . ⊂ . be a linear operator in . and let . (.) be an . valued function. In this chapter we will study the initial value problem ..
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Some Nonlinear Evolution Equations,In this section we will study the following semilinear initial value problem: . where . is the infinitesimal generator of a C.semigroup . 0, on a Banach space . and .: .. X . is continuous in . and satisfies a Lipschitz condition in
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