Description
This revised second edition of Christopher Sogge’s 1995 work provides a selfcontained 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 KlainermanSobolev inequalities and weighted spacetime 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 R^{1+3} is discussed with blowup 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 ChristKiselev lemma are given, the material being new in this edition. Using the Strichartz estimates, the critical wave equation in R^{1+3} is studied.
Publications
Pub. Date 
ISBN13 
ISBN10 
Medium 
Binding 
Size, Etc. 
Status 
List Price 
2013 Oct 
9781571462794 
1571462791 
paperback 
7” x 10” 
In Print 
US$58.50 

2008 Aug 
9781571461735 
1571461736 
hardcover 
7” x 10” 
Out of Print 
US$69.00 