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Blowup for Nonlinear Hyperbolic Equations de Serge Alinhac

Blowup for Nonlinear Hyperbolic Equations: Progress in Nonlinear Differential Equations and Their Applications, cartea 17

Autor Serge Alinhac
en Limba Engleză Paperback – 26 sep 2011

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Specificații

ISBN-13: 9781461275886
ISBN-10: 1461275881
Pagini: 132
Ilustrații: 113 p.
Dimensiuni: 155 x 235 x 7 mm
Greutate: 0.2 kg
Ediția:Softcover reprint of the original 1st ed. 1995
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Progress in Nonlinear Differential Equations and Their Applications

Locul publicării:Boston, MA, United States

Public țintă

Research

Cuprins

I. The Two Basic Blowup Mechanisms.- A. The ODE mechanism.- B. The geometric blowup mechanism.- C. Combinations of the two mechanisms.- Notes.- II. First Concepts on Global Cauchy Problems.- 1. Short time existence.- 2. Lifespan and blowup criterion.- 3. Blowup or not? Functional methods.- 4. Blowup or not? Comparison and averaging methods.- Notes.- III. Semilinear Wave Equations.- 1. Semilinear blowup criteria.- 2. Maximal influence domain.- 3. Maximal influence domains for weak solutions.- 4. Blowup rates at the boundary of the maximal influence domain.- 5. An example of a sharp estimate of the lifespan.- Notes.- IV. Quasilinear Systems in One Space Dimension.- 1. The scalar case.- 2. Riemann invariants, simple waves, and L1-boundedness.- 3. The case of 2 × 2 systems.- 4. General systems with small data.- 5. Rotationally invariant wave equations.- Notes.- V. Nonlinear Geometrical Optics and Applications.- 1. Quasilinear systems in one space dimension.- 2. Quasilinear wave equations.- 3. Further results on the wave equation.- Notes.