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.

*"synopsis" may belong to another edition of this title.*

The main subject of this book is the generalization of the Cauchy-Kovalevska theorem. Solutions of initial value problems are given for the cases where the initial functions are generalized analytic functions. Two methods are employed in order to obtain the generalizations: the method of Banach space scales and a modification of W. Walters's elementary proof of the calssical theorem by Cauchy-Kovalevska. Students can use the book as an introduction and researchers can find in it , an summery of mew generalization of CauchyKovalevska problems.

Text: English

Introduction: French, German, Russian

*"About this title" may belong to another edition of this title.*

US$ 81.88

**Shipping:**
US$ 9.94

From United Kingdom to U.S.A.

Published by
Springer
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Springer, 1989. Paperback. Book Condition: NEW. 9783540502166 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Bookseller Inventory # HTANDREE0420696

More Information About This Seller | Ask Bookseller a Question

Published by
Springer
(2016)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Springer, 2016. Paperback. Book Condition: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Bookseller Inventory # ria9783540502166_lsuk

More Information About This Seller | Ask Bookseller a Question

Published by
Springer-Verlag Berlin and Heidelberg GmbH and Co. KG
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Quantity Available: > 20

Seller

Rating

**Book Description **Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 1989. PAP. Book Condition: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # LQ-9783540502166

More Information About This Seller | Ask Bookseller a Question

Published by
Springer-Verlag Berlin and Heidelberg GmbH and Co. KG
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Quantity Available: > 20

Seller

Rating

**Book Description **Springer-Verlag Berlin and Heidelberg GmbH and Co. KG, 1989. PAP. Book Condition: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Bookseller Inventory # IP-9783540502166

More Information About This Seller | Ask Bookseller a Question

Published by
Springer
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 1

Seller

Rating

**Book Description **Springer, 1989. Paperback. Book Condition: New. book. Bookseller Inventory # 3540502165

More Information About This Seller | Ask Bookseller a Question

Published by
Springer
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 10

Seller

Rating

**Book Description **Springer, 1989. Paperback. Book Condition: New. This item is printed on demand. Bookseller Inventory # INGM9783540502166

More Information About This Seller | Ask Bookseller a Question

Published by
Springer
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Softcover
Quantity Available: 15

Seller

Rating

**Book Description **Springer, 1989. Book Condition: New. This item is printed on demand for shipment within 3 working days. Bookseller Inventory # LP9783540502166

More Information About This Seller | Ask Bookseller a Question

Published by
Springer
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 2

Seller

Rating

**Book Description **Springer, 1989. Paperback. Book Condition: Brand New. In Stock. Bookseller Inventory # x-3540502165

More Information About This Seller | Ask Bookseller a Question

Published by
Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany
(1989)

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: > 20

Seller

Rating

**Book Description **Springer-Verlag Berlin and Heidelberg GmbH Co. KG, Germany, 1989. Paperback. Book Condition: New. 201 x 135 mm. Language: English . Brand New Book ***** Print on Demand *****.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. Bookseller Inventory # AAV9783540502166

More Information About This Seller | Ask Bookseller a Question

Published by
Springer

ISBN 10: 3540502165
ISBN 13: 9783540502166

New
Paperback
Quantity Available: 20

Seller

Rating

**Book Description **Springer. Paperback. Book Condition: New. Paperback. 188 pages. The main subject of this book is the generalization of the Cauchy-Kovalevska theorem. Solutions of initial value problems are given for the cases where the initial functions are generalized analytic functions. Two methods are employed in order to obtain the generalizations: the method of Banach space scales and a modification of W. Walterss elementary proof of the calssical theorem by Cauchy-Kovalevska. Students can use the book as an introduction and researchers can find in it , an summery of mew generalization of CauchyKovalevska problems. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Bookseller Inventory # 9783540502166

More Information About This Seller | Ask Bookseller a Question