Racke Lectures on Nonlinear Evolution Equations

Initial Value Problem
1992
ISBN: 978-3-663-10629-6
Verlag: Vieweg & Teubner
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 19, 260 Seiten, eBook

Reihe: Aspects of Mathematics

This book serves as an elementary, self contained introduction into some important aspects of the theory of global solutions to initial value problems for nonlinear evolution equations. The presentation is made using the classical method of continuation of local solutions with the help of a priori estimates obtained for small data.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Racke, Reinhard

Inhaltsverzeichnis

1 Global solutions to wave equations — existence theorems.- 2 Lp-Lq-decay estimates for the linear wave equation.- 3 Linear symmetric hyperbolic systems.- 4 Some inequalities.- 5 Local existence for quasilinear symmetric hyperbolic systems.- 6 High energy estimates.- 7 Weighted a priori estimates for small data.- 8 Global solutions to wave equations — proofs.- 9 Other methods.- 10 Development of singularities.- 11 More evolution equations.- 12 Further aspects and questions.- A Interpolation.- B The Theorem of Cauchy-Kowalevsky.- C A local existence theorem for hyperbolic-parabolic systems.- References.- Notation.

Über Autor(innen)

Dr. Reinhard Racke, Institut für Angewandte Mathematik,Universität Bonn/ Prof. Dr. Klas Diederich, Mathematisches Institut der Universität Wuppertal.