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 subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. 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 g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.

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Bibliographic Information

Book Title: Existence Families, Functional Calculi and Evolution Equations
Authors: Ralph deLaubenfels
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0073401
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1994
Softcover ISBN: 978-3-540-57703-4Published: 28 March 1994
eBook ISBN: 978-3-540-48322-9Published: 15 November 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVI, 244
Topics: Analysis

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Table of contents (31 chapters)

Front Matter

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