Lectures on Non-Linear Wave Equations

Christopher D. Sogge

ISBN 10: 1571462791 / ISBN 13: 9781571462794

Editore: International Press of Boston, Incorporated, 2013

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pp. 214 2nd Edition.

Codice articolo 26142326038

Dati bibliografici

• Titolo: Lectures on Non-Linear Wave Equations
• Editore: International Press of Boston, Incorporated
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 1571462791
• ISBN 13: 9781571462794
• Rilegatura: Brossura
• Condizione: Used

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Riassunto

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.