User menu

Shopping cart

The Mathematics of Shock Reflection-Diffraction and Von Neumann's Conjectures: (Ams-197) (Annals of Mathematics Studies #197) (Hardcover)

The Mathematics of Shock Reflection-Diffraction and Von Neumann's Conjectures: (Ams-197) (Annals of Mathematics Studies #197) Cover Image
Hard to Find - Contact Store for Availability


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.

About the Author

Gui-Qiang G. Chen is the Statutory Professor in the Analysis of Partial Differential Equations at the Mathematical Institute of the University of Oxford, where he is also professorial fellow at Keble College. Mikhail Feldman is professor of mathematics at the University of Wisconsin-Madison.

Product Details
ISBN: 9780691160542
ISBN-10: 0691160546
Publisher: Princeton University Press
Publication Date: February 27th, 2018
Pages: 832
Language: English
Series: Annals of Mathematics Studies
ABA Admin Product Details
Data Source: Ingram
Created At: 11/12/2016 02:57pm
Last Updated At: 1/15/2022 10:34am