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Binding: HardcoverDewey Decimal Number: 515 EAN: 9781571461735 Edition: second ISBN: 1571461736 Label: International Press of Boston Manufacturer: International Press of Boston Number Of Items: 1 Number Of Pages: 203 Publication Date: July 31, 2008 Publisher: International Press of Boston Studio: International Press of Boston Editorial Review: Product Description: 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 |
