ENGLISH

Existence Families, Functional Calculi and Evolution Equations

By Ralph DeLaubenfels

Book information

Publisher
Springer
Year
1994
ISBN
3540577033, 9783540577034
Language
english
Format
DJVU
Filesize
1 MB (1442197 bytes)
Series
Lecture Notes in Mathematics
Edition
1
Pages
272\272
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

Description

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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