Vanishing viscosity limit for a class of hyperbolic systems in 1-d with nonlinear viscosity

Title: Vanishing viscosity limit for a class of hyperbolic systems in 1-d with nonlinear viscosity 

Abstract: The vanishing viscosity method is a way to construct and select physically relevant solutions for hyperbolic conservation laws. In this talk, we will consider a class of hyperbolic systems in one space dimension with a nonlinear viscosity matrix. First, we prove the global existence of smooth solutions to the parabolic equation for initial data with a small total variation. We show that the solution to the parabolic equation converges to a semi-group solution of the hyperbolic system as viscosity goes to zero. Furthermore, we prove that the limit coincides with the one obtained when the viscosity matrix is the identity matrix. This talk is based on a joint work with Boris Haspot.