000			nam a22 4500
999			_c32842 _d32842
008			240219b xxu||||| |||| 00| 0 eng d
020			_a9780691160559
082			_a531.1133 _bCHE
100			_aChen, Gui-Qiang
245			_aThe Mathematics of Shock Reflection-Diffraction and von Neumann's Conjectures
260			_bPrinceton University Press, _aPrinceton : _c2018
300			_axiv, 814 p. ; _bill., _c24 cm.
365			_b84.00 _c$ _d86.50
490			_aAnnals of mathematics studies _vv.197
504			_aIncludes bibliographical references and index.
520			_aThis 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.
650			_aA priori estimated
650			_aAccuracy and precision
650			_aAlgorithm
700			_aFeldman, Mikhail
942			_2ddc _cBK