Solution of Initial Value Problems in Classes of Generalized Analytic Functions.

Tutschke, Wolfgang.

ISBN 10: 3540502165 / ISBN 13: 9783540502166

Editore: Berlin / Heidelberg / New York / London / Paris / Tokyo, Springer-Verlag, 1989

Riguardo questo articolo

20.5 × 13.5 cm, softcover, 188 pages, text in English, very good condition, see picture. First edition. A specialized monograph on the Cauchy problem in classes of generalized analytic functions, combining methods from partial differential equations and complex analysis, with applications to mathematical physics. 220g.

Codice articolo 80667

Dati bibliografici

• Titolo: Solution of Initial Value Problems in Classes of Generalized Analytic Functions.
• Editore: Berlin / Heidelberg / New York / London / Paris / Tokyo, Springer-Verlag
• Data di pubblicazione: 1989
• Lingua: Inglese
• ISBN 10: 3540502165
• ISBN 13: 9783540502166
• Rilegatura: Brossura
• Edizione: prima edizione
• Peso: 220 grammi
• Cataloghi dei venditori:
  • Wiskunde

Descrizione articolo

Riassunto

The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend­ ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con­ cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.

Contenuti

0. Introduction.- 1. Initial Value Problems in Banach Spaces.- 2. Scales of Banach Spaces.- 3. Solution of Initial Value Problems in Scales of Banach Spaces.- 4. The Classical Cauchy-Kovalevskaya Theorem.- 5. The Holmgren Theorem.- 6. Basic Properties of Generalized Analytic Functions.- 7. Initial Value Problems with Generalized Analytic Initial Functions.- 8. Contraction-Mapping Principles in Scales of Banach Spaces.- 9. Further Existence Theorems for Initial Value Problems in Scales of Banach Spaces.- 10. Further Uniqueness Theorems.- References.