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

Gui-Qiang G. Chen University of Oxford Miklhail Feldman University of Wiscosin-Madison

Analysis of PDEs mathscidoc:2104.14001

830, 2018
The purpose of this research monograph is to survey some recent developments in the analysis of shock reflection-diffraction, to present our original mathematical proofs of von Neumann’s conjectures for potential flow, to collect most of the related results and new techniques in the analysis of partial differential equations achieved in the last decades, and to discuss a set of fundamental open problems relevant to the directions of future research in this and related areas.
Shock reflection-diffraction, free boundaries, von Neumann conjectures
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  • In this original research monograph, the von Neumann's conjectures (the detachment conjecture, the sonic conjecture) were solved for shock reflection-diffraction for potential flow via solving the corresponding free boundary problems involving transonic shock waves for nonlinear PDEs of mixed elliptic-hyperbolic type.n
  title={The Mathematics of Shock Reflection-Diffraction and von Neumann's conjectures},
  author={Gui-Qiang G. Chen, and Miklhail Feldman},
Gui-Qiang G. Chen, and Miklhail Feldman. The Mathematics of Shock Reflection-Diffraction and von Neumann's conjectures. 2018. pp.830.
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