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Book Synopsis

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 lawsPDEs 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 nonlin

The Mathematics of Shock ReflectionDiffraction

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    A Paperback / softback by Gui-Qiang Chen, Mikhail Feldman

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      Publisher: Princeton University Press
      Publication Date: 27/02/2018
      ISBN13: 9780691160559, 978-0691160559
      ISBN10: 0691160554
      Also in:
      Mathematics Mathematical / Computational / Theoretical physics

      Description

      Book Synopsis

      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 lawsPDEs 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 nonlin

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