Archive for Rational Mechanics and Analysis

, Volume 211, Issue 1, pp 61–112 | Cite as

Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

  • Gui-Qiang ChenEmail author
  • Xuemei Deng
  • Wei Xiang


We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow, through the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order with a degenerate oblique derivative boundary condition. We establish a global theory of existence and optimal regularity for this shock diffraction problem. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.


Free Boundary Problem Wedge Angle Optimal Regularity Shock Diffraction Oblique Derivative Problem 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.School of Mathematical SciencesFudan UniversityShanghaiChina
  3. 3.Department of MathematicsNorthwestern UniversityEvanstonUSA
  4. 4.College of ScienceChina Three Gorges UniversityYichangChina
  5. 5.School of Mathematical SciencesXiamen UniversityXiamenChina

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