The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures By: Gui-Qiang G Chen; Mikhail Feldman Publisher: Princeton University Press Print ISBN: 9780691160559, 0691160554 eText ISBN: 9781400885435, 1400885434 Copyright year: 2018 Format: PDF Available from $ 75.00 USD SKU 9781400885435 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. Additional ISBNs 9780691160542, 0691160546 Download now: https://ouo.io/ZNlr7x
