Chapters in this book

1. Frontmatter Cover
2. Contents v
3. Preface xi
4. Part I: Shock Reflection-Diffraction, Nonlinear Conservation Laws of Mixed Type, and von Neumann’s Conjectures
5. 1. Shock Reflection-Diffraction, Nonlinear Partial Differential Equations of Mixed Type, and Free Boundary Problems 3
6. 2. Mathematical Formulations and Main Theorems 16
7. 3. Main Steps and Related Analysis in the Proofs of the Main Theorems 37
8. Part II: Elliptic Theory and Related Analysis for Shock Reflection-Diffraction
9. 4. Relevant Results for Nonlinear Elliptic Equations of Second Order 69
10. 5. Basic Properties of the Self-Similar Potential Flow Equation 216
11. Part III: Proofs of the Main Theorems for the Sonic Conjecture and Related Analysis
12. 6. Uniform States and Normal Reflection 231
13. 7. Local Theory and von Neumann’s Conjectures 242
14. 8. Admissible Solutions and Features of Problem 2.6.1 281
15. 9. Uniform Estimates for Admissible Solutions 319
16. 10. Regularity of Admissible Solutions away from the Sonic Arc 382
17. 11. Regularity of Admissible Solutions near the Sonic Arc 396
18. 12. Iteration Set and Solvability of the Iteration Problem 440
19. 13. Iteration Map, Fixed Points, and Existence of Admissible Solutions up to the Sonic Angle 524
20. 14. Optimal Regularity of Solutions near the Sonic Circle 586
21. Part IV: Subsonic Regular Reflection-Diffraction and Global Existence of Solutions up to the Detachment Angle
22. 15. Admissible Solutions and Uniform Estimates up to the Detachment Angle 615
23. 16. Regularity of Admissible Solutions near the Sonic Arc and the Reflection Point 629
24. 17. Existence of Global Regular Reflection-Diffraction Solutions up to the Detachment Angle 690
25. Part V: Connections and Open Problems
26. 18. The Full Euler Equations and the Potential Flow Equation 757
27. 19. Shock Reflection-Diffraction and New Mathematical Challenges 785
28. Bibliography 794
29. Index 815