CONTRACTIVE RELAXATION SYSTEMS AND INTERACTING PARTICLES FOR SCALAR CONSERVATION-LAWS

We consider a class of semilinear hyperbolic systems with relaxation t hat are contractive in the L(1)-norm and admit invariant regions. We s how that, as the relaxation parameter epsilon goes to zero, their solu tions converge to a weak solution of the scalar multidimensional conse rvation law that satisfies the Kruzhkov conditions. In the case of one space dimension, we propose certain interacting particle systems, who se mesoscopic limit is the systems with relaxation and their macroscop ic dynamics is described by entropy solutions of a scalar conservation law.