E-Book, Englisch, Band 17, 113 Seiten, eBook
Reihe: Progress in Nonlinear Differential Equations and Their Applications
Alinhac Blowup for Nonlinear Hyperbolic Equations
Erscheinungsjahr 2013
ISBN: 978-1-4612-2578-2
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, Band 17, 113 Seiten, eBook
Reihe: Progress in Nonlinear Differential Equations and Their Applications
ISBN: 978-1-4612-2578-2
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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.
