Singular Nonlinear Partial Differential Equations

Raymond Gérard

ISBN 10: 3322802868 / ISBN 13: 9783322802866

Published by Springer, Berlin, Vieweg+Teubner Dez 2011, 2011

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -The aim of this book is to put together all the results that are known about the existence of formal, holomorphic and singular solutions of singular non linear partial differential equations. We study the existence of formal power series solutions, holomorphic solutions, and singular solutions of singular non linear partial differential equations. In the first chapter, we introduce operators with regular singularities in the one variable case and we give a new simple proof of the classical Maillet's theorem for algebraic differential equations. In chapter 2, we extend this theory to operators in several variables. The chapter 3 is devoted to the study of formal and convergent power series solutions of a class of singular partial differential equations having a linear part, using the method of iteration and also Newton's method. As an appli cation of the former results, we look in chapter 4 at the local theory of differential equations of the form xy' = 1(x,y) and, in particular, we show how easy it is to find the classical results on such an equation when 1(0,0) = 0 and give also the study of such an equation when 1(0,0) #- 0 which was never given before and can be extended to equations of the form Ty = F(x, y) where T is an arbitrary vector field. 272 pp. Englisch.

Seller Inventory # 9783322802866

Bibliographic Details

• Title: Singular Nonlinear Partial Differential Equations
• Publisher: Springer, Berlin, Vieweg+Teubner Dez 2011
• Publication Date: 2011
• Language: English
• ISBN 10: 3322802868
• ISBN 13: 9783322802866
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 240W x 160H x 15D millimeters 240 millimeters width by 160 millimeters height by 15 millimeters depth
• Weight: 455 grams

About this title

Synopsis

Das Anliegen dieser mathematischen Monographie ist die Zusammenfassung aller Resultate, die heutzutage vorliegen über die Existenz formaler, holomorpher oder singulärer Lösungen von singulären nicht-linearen partiellen Differentialgleichungen.

About the Author

Prof. Raymond Gerard ist am Institut de Recherche Mathématique Alsacien an der Université Louis Pasteur in Strasbourg beschäftigt. Prof. Hidetoshi Tahara lehrt an der Sophia Universität in Tokyo.