Evolution Equations in Scales of Banach Spaces (TeubnerTexte zur Mathematik) (Teubner-Texte zur Mathematik, 140, Band 140)

Konietzko, Nikolaus, C. Medici Tullio und Oliver Caps:

ISBN 10: 3519003767 / ISBN 13: 9783519003762

Published by Teubner Verlag, 2002

About this Item

312 Seiten Alle Bücher & Medienartikel von Book Broker sind stets in gutem & sehr gutem gebrauchsfähigen Zustand. Dieser Artikel weist folgende Merkmale auf: Helle/saubere Seiten in fester Bindung. Sprache: Englisch Gewicht in Gramm: 540 Taschenbuch, Größe: 16.8 x 1.8 x 23.8 cm Softcover reprint of the original 1st ed. 2002.

Seller Inventory # 660995893

Bibliographic Details

• Title: Evolution Equations in Scales of Banach Spaces (TeubnerTexte zur Mathematik) (Teubner-Texte zur Mathematik, 140, Band 140)
• Publisher: Teubner Verlag
• Publication Date: 2002
• Language: English
• ISBN 10: 3519003767
• ISBN 13: 9783519003762
• Binding: Soft cover
• Condition: Sehr gut
• Weight: 540 grams
• Seller catalogs:
  • Varia

About this title

Synopsis

The book provides a new functional-analytic approach to evolution equations by considering the abstract Cauchy problem in a scale of Banach spaces. The usual functional analytic methods for studying evolution equations are formu­ lated within the setting of unbounded, closed operators in one Banach space. This setting is not adapted very well to the study of many pseudo differential and differential equations because these operators are naturally not given as closed, unbounded operators in one Banach space but as continuous opera­ tors in a scale of function spaces. Thus, applications within the setting of unbounded, closed operators require a considerable amount of additional work because one has to construct suitable closed realizations of these operators. This choice of closed realizations is technically complicated even for simple applications. The main feature of the new functional analytic approach of the book is to study the operators in scales of Banach spaces that are constructed by simple reference operators. This is a natural setting for many operators acting in scales of function spaces. The operators are only expected to respect the scale and to satisfy certain inequalities but we can avoid completely the choice of any closed realization of these operators which is of great importance in applications. We use the mapping properties of the reference operators to prove sufficient conditions for well-posedness of linear and quasilinear Cauchy problems. In the linear, time-dependent case these conditions are shown to characterize well-posedness. A similar result in the standard setting (i. e.

About the Author

Dr. Oliver Caps, Universität Mainz