The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
eBook - PDF

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

  1. 832 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures

About this book

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 differential equations (PDEs), as well as a set of fundamental open problems for further development.

Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws—PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs—mixed type, free boundaries, and corner singularities—that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.

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Yes, you can access The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures by Gui-Qiang G Chen,Mikhail Feldman in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. I Shock Reflection-Diffraction, Nonlinear Conservation Laws of Mixed Type, and von Neumann’s Conjectures
  7. II Elliptic Theory and Related Analysis for Shock Reflection-Diffraction
  8. III Proofs of the Main Theorems for the Sonic Conjecture and Related Analysis
  9. IV Subsonic Regular Reflection-Diffraction and Global Existence of Solutions up to the Detachment Angle
  10. V Connections and Open Problems
  11. Bibliography
  12. Index