Front Matter....Pages i-xxi
Front Matter....Pages 1-1
Ill-Posed Problems....Pages 3-12
Characteristics and Initial-Value Problems....Pages 13-16
The One-Dimensional Wave Equation....Pages 17-25
Uniqueness and Energy Integrals....Pages 26-32
Holmgren’s Uniqueness Theorem....Pages 33-38
An Initial-Value Problem for a Hyperbolic Equation....Pages 39-44
Distribution Theory....Pages 45-63
Second-Order Linear Elliptic Equations....Pages 64-77
Second-Order Linear Parabolic Equations....Pages 78-90
Front Matter....Pages 91-91
Comparison Theorems and Monotonicity Methods....Pages 93-105
Linearization....Pages 106-125
Topological Methods....Pages 126-166
Bifurcation Theory....Pages 167-191
Systems of Reaction—Diffusion Equations....Pages 192-236
Front Matter....Pages 237-237
Discontinuous Solutions of Conservation Laws....Pages 239-264
The Single Conservation Law....Pages 265-305
The Riemann Problem for Systems of Conservation Laws....Pages 306-336
Applications to Gas Dynamics....Pages 337-367
The Glimm Difference Scheme....Pages 368-390
Riemann Invariants, Entropy, and Uniqueness....Pages 391-425
Front Matter....Pages 237-237
Quasi-Linear Parabolic Systems....Pages 426-444
Front Matter....Pages 445-445
The Conley Index....Pages 447-477
Index Pairs and the Continuation Theorem....Pages 478-506
Travelling Waves....Pages 507-555
Back Matter....Pages 557-584