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Existence families, functional calculi, and evolution equations

Author: Ralph DeLaubenfels
Publisher: Berlin ; New York : Springer-Verlag, ©1994.
Series: Lecture notes in mathematics (Springer-Verlag), 1570.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
DeLaubenfels, Ralph, 1951-
Existence families, functional calculi, and evolution equations.
Berlin ; New York : Springer-Verlag, ©1994
(DLC) 93047576
(OCoLC)29595385
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ralph DeLaubenfels
ISBN: 9783540483229 3540483225
OCLC Number: 289103357
Reproduction Notes: Electronic reproduction. [S.l.] : HathiTrust Digital Library, 2010. MiAaHDL
Description: 1 online resource (xv, 234 pages).
Details: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Contents: I. Intuition and Elementary Examples --
II. Existence Families --
III. Regularized Semigroups --
IV. The Solution Space of an Operator and Automatic Well-Posedness --
V. Exponentially Bounded (Banach) Solution Space --
VI. Well-posedness on a Larger Space; Generalized Solutions --
VII. Entire Vectors and Entire Existence Families --
VIII. Reversibility of Parabolic Problems --
IX. The Cauchy Problem for the Laplace Equation --
X. Boundary Values of Holomorphic Semigroups --
XI. The Schrodinger Equation --
XII. Functional Calculus for Commuting Generators of Bounded Strongly Continuous Groups --
XIII. Petrovsky Correct Matrices of Generators of Bounded Strongly Continuous Groups --
XIV. Arbitrary Matrices of Generators of Bounded Strongly Continuous Groups --
XV. More Examples of Regularized Semigroups --
XVI. Existence and Uniqueness Families --
XVII. C-resolvents and Hille-Yosida Type Theorems --
XVIII. Relationship to Integrated Semigroups --
XIX. Perturbations --
XX. Type of an Operator. XXI. Holomorphic C-existence Families --
XXII. Unbounded Holomorphic Functional Calculus for Operators with Polynomially Bounded Resolvents --
XXIII. Spectral Conditions Guaranteeing Solutions of the Abstract Cauchy Problem --
XXIV. Polynomials of Generators --
XXV. Iterated Abstract Cauchy Problems --
XXVI. Equipartition of Energy --
XXVII. Simultaneous Solution Space --
XXVIII. Exponentially Bounded Simultaneous Solution Space --
XXIX. Simultaneous Existence Families --
XXX. Simultaneous Existence Families for Matrices of Operators --
XXXI. Time Dependent Evolution Equations.
Series Title: Lecture notes in mathematics (Springer-Verlag), 1570.
Responsibility: Ralph deLaubenfels.

Abstract:

One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of  Read more...

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