Items related to Lectures on Non-Linear Wave Equations
Synopsis
This much-anticipated revised second edition of Christopher Sogge's 1995 work provides a self-contained account of the basic facts concerning the linear wave equation and the methods from harmonic analysis that are necessary when studying nonlinear hyperbolic differential equations. Sogge examines quasilinear equations with small data where the Klainerman-Sobolev inequalities and weighted space-time estimates are introduced to prove global existence results. New simplified arguments are given in the current edition that allow one to handle quasilinear systems with multiple wave speeds. The next topic concerns semilinear equations with small initial data. John's existence theorem for R1+3 is discussed with blow-up problems and some results for the spherically symmetric case. After this, general Strichartz estimates are treated. A proof of the endpoint Strichartz estimates of Keel and Tao and the Christ-Kiselev lemma are given, the material being new in this edition. Using the Strichartz estimates, the critical wave equation in R1+3 is studied.
Table of contents
Chapter 1: Background and groundwork
Chapter 2: Quasilinear equations with small data
Chapter 3: Semilinear equations with small data
Chapter 4: General Strichartz estimates
Chapter 5: Global existence for semilinear equations with large data
Appendix: Some tools from classical analysis
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About the Author
Christopher Sogge is currently a Professor at the Johns Hopkins University.
"About this title" may belong to another edition of this title.
- PublisherIntl Pr of Boston Inc
- Publication date2008
- ISBN 10 1571461736
- ISBN 13 9781571461735
- BindingHardcover
- LanguageEnglish
- Edition number2
- Number of pages203
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