Viscous approximation of initial-boundary value problems for systems of conservation laws in one space dimension

In the first part of the seminar I will overview some results concerning one-dimensional systems of conservation laws and viscous approximations of initial-boundary value problems. The main challenges posed by the initial-boundary value problem are the possible presence of boundary layer phenomena and the fact that, in general, the limits of two different viscous approximation do not coincide.

In the second part of the seminar I will focus on results, obtained in collaboration with S. Bianchini and C. Christoforou, concerning the limit of a viscous approximation in the case of the so-called boundary Riemann problem. In particular, I will describe a possible characterization of the limit and I I will establish a uniqueness criterium.