Plenary Lecture

Hyperbolic Conservation Laws: Theory and Numerical Simulations of Shock Reflection

Assistant Professor Katarina Jegdic
Computer and Mathematical Sciences
University of Houston - Downtown
USA

Abstract: The first part of this talk is a brief introduction to the systems of partial differential equations known as conservation laws. We will discuss the physical background of these systems and show several applications. Notions of weak solutions and entropy conditions will be outlined.
The second part of the talk is on analysis of two-dimensional Riemann problems for systems of conservation laws with applications to shock reflection. When written in self-similar coordinates, these problems lead to free boundary problems for the reflected shock and a subsonic state behind the shock. We will present our recent results (joint work with Barbara Lee Keyfitz and Suncica Canic) on analysis of these problems for the isentropic gas dynamics equations using the theory of second order elliptic equations with mixed boundary conditions and fixed point theory. The talk will conclude with numerical solutions to several Riemann problems for the full gas dynamics equations resulting in weak and strong regular reflection.

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 fall of 2006. Her research interests are in mathematical and numerical analysis of systems of conservation laws with applications to shock reflection and petroleum engineering.