Название: The Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
Автор: Gui-Qiang G Chen, Mikhail Feldman
Издательство: Princeton University Press
Год: 2018
ISBN: 9780691160542
Серия: Annals of Mathematics Studies (Book 191)
Формат: pdf
Страниц: 832
Размер: 10,8 mb
Язык: English

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.