DFG Priority Research Program ANumE on
Analysis and numerics of conservation laws

Research Project

Viscous profiles for systems of conservation laws

Research directors

Prof. Dr. Bernold Fiedler

Dr. Jörg Härterich

Members

Dr. Stefan Liebscher

Summary

The viscosity criterion is very important for the choice of physically correct solutions to systems of hyperbolic conservation laws: A solution of the hyperbolic equation is admissible if it can be approximated by a sequence of solutions of parabolic equations where the viscosity tends to 0. In the case of shock waves, traveling wave solutions of the viscous equation are expected as approximating solutions. Thereby, the problem is reduced to the investigation of heteroclinic orbits and bifurcations in a finite-dimensional system with parameters. These parameters represent the states of the associated Riemann problem and the shock speed.

The main goal of this project is the understanding of some parts of the huge variety of phenomena which are connected to the interplay of physically motivated viscous approximations with stiff source terms. Thereby we focus our attention on the existence and stability of oscillating shocks.

Besides this, a complete description of global attractors of scalar balance laws with periodic initial conditions is intended.