The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures : : (AMS-197) /

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures : : (AMS-197) / / Mikhail Feldman, Gui-Qiang Chen.

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differenti...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2018 English
VerfasserIn:
Chen, Gui-Qiang,
Feldman, Mikhail,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2018]
©2018
Year of Publication:2018
Language:English
Series:Annals of Mathematics Studies ; 197
Online Access:
Physical Description:1 online resource (832 p.) :; 35 line illus.
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Table of Contents:
  • Frontmatter
  • Contents
  • Preface
  • Part I: Shock Reflection-Diffraction, Nonlinear Conservation Laws of Mixed Type, and von Neumann's Conjectures
  • 1. Shock Reflection-Diffraction, Nonlinear Partial Differential Equations of Mixed Type, and Free Boundary Problems
  • 2. Mathematical Formulations and Main Theorems
  • 3. Main Steps and Related Analysis in the Proofs of the Main Theorems
  • Part II: Elliptic Theory and Related Analysis for Shock Reflection-Diffraction
  • 4. Relevant Results for Nonlinear Elliptic Equations of Second Order
  • 5. Basic Properties of the Self-Similar Potential Flow Equation
  • Part III: Proofs of the Main Theorems for the Sonic Conjecture and Related Analysis
  • 6. Uniform States and Normal Reflection
  • 7. Local Theory and von Neumann's Conjectures
  • 8. Admissible Solutions and Features of Problem 2.6.1
  • 9. Uniform Estimates for Admissible Solutions
  • 10. Regularity of Admissible Solutions away from the Sonic Arc
  • 11. Regularity of Admissible Solutions near the Sonic Arc
  • 12. Iteration Set and Solvability of the Iteration Problem
  • 13. Iteration Map, Fixed Points, and Existence of Admissible Solutions up to the Sonic Angle
  • 14. Optimal Regularity of Solutions near the Sonic Circle
  • Part IV: Subsonic Regular Reflection-Diffraction and Global Existence of Solutions up to the Detachment Angle
  • 15. Admissible Solutions and Uniform Estimates up to the Detachment Angle
  • 16. Regularity of Admissible Solutions near the Sonic Arc and the Reflection Point
  • 17. Existence of Global Regular Reflection-Diffraction Solutions up to the Detachment Angle
  • Part V: Connections and Open Problems
  • 18. The Full Euler Equations and the Potential Flow Equation
  • 19. Shock Reflection-Diffraction and New Mathematical Challenges
  • Bibliography
  • Index

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