Plenary Lecture

Plenary Lecture

Shock Reflection Problems and Gas Dynamics Equations

Assistant Professor Katarina Jegdic
Computer and Mathematical Sciences Department
University of Houston
Downtown Houston, TX 77002

Abstract: We present mathematical analysis of shock reflection phenomenon using two-dimensional systems of conservation laws. Depending on the initial data, various types of shock reflection are possible, such as regular reflection (either supersonic or transonic) or Mach. We present proof of existence of regular reflection for the system of isentropic gas dynamics equations. The main idea in our approach is to rewrite the system using the self-similar coordinates. This leads to a free boundary problem for the subsonic state and the reflected shock. Existence of a solution is proved using the Holder estimates for the second order elliptic equations and various fixed point arguments. This work is joint with Barbara Lee Keyfitz (Ohio State University) and Suncica Canic (University of Houston).

Brief Biography of the Speaker:
Katarina Jegdic received B. Sc. degree in Mathematics from the University of Novi Sad, Serbia, in 1997. She obtained M.S. degree and Ph.D. degree in Mathematics from the University of Illinois at Urbana-Champaign, USA, in 2000 and 2004, respectively, after which she held a postdoctoral position at the University of Houston, USA. She is an assistant professor at the University of Houston - Downtown since 2006. Her research interests are in mathematical and numerical analysis of systems of conservation laws with applications to aerodynamics.

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