CHAPTER I. The Two Basic Blowup Mechanisms
Introduction
A. The ODE mechanism
B. The geometric blowup mechanism
C. Combinations of the two mechanisms
Notes
CHAPTER II. First Concepts on Global Cauchy Problems
Introduction
1. Short time existence
2. Lifespan and blowup criterion
3. Blowup or not? Functional methods
4. Blowup or not? Comparison and averaging methods
Notes
CHAPTER III. Semilinear Wave Equations
Introduction
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
CHAPTER IV. Quasilinear Systems in One Space Dimension
Introduction
1. The scalar case
2. Riemann invariants, simple waves, and L1-boundedness
3. The case of 2 x 2 systems
4. General systems with small data
5. Rotationally invariant wave equations
Notes
CHAPTER V. Nonlinear Geometrical Optics and Applications
Introduction
1. Quasilinear systems in one space dimension
2. Quasilinear wave equations
3. Further results on the wave equation
BIBLIOGRAPHY
INDEX
Notes
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