Blowup for Nonlinear Hyperbolic Equations [electronic resource] /

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.

Bibliographic Details

Main Authors:	Alinhac, Serge. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Boston, MA : Birkhäuser Boston, 1995
Subjects:	Mathematics., Mathematical analysis., Analysis (Mathematics)., Partial differential equations., Partial Differential Equations., Analysis.,
Online Access:	http://dx.doi.org/10.1007/978-1-4612-2578-2
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