Special Session 15: Qualitative properties for solutions to nonlinear elliptic and parabolic equations

Global existence and zero relaxation limit for a hyperbolic system arising in traffic flow with large data
Tong Li
University of Iowa
USA
Co-Author(s):    Jose David Beltran
Abstract:
This talk is concerned with the existence of global weak solutions and their zero relaxation limit for a non-strictly hyperbolic system arising in traffic flow with large initial data. We use the vanishing viscosity method and the compensated compactness framework to prove the existence of admissible weak solutions and to study their behavior as the relaxation parameter tends to zero. By constructing convex dissipative entropies that display special compatibility conditions with the local equilibrium equation of the system, we establish the existence and uniqueness of the zero relaxation limit solution for large initial data.