On the L2 and L1 convergence rates of viscous solutions of the Keyfitz-Kranzer system with piecewise smooth and large BV data

We study the zero-dissipation problem of the Keyfitz-Kranzer system in L2 and L1 spaces. When the solution of the inviscid problem is piecewise smooth and has finitely many noninteracting shocks with finite strength, there exists, for each ε (the viscosity), unique solution to the viscous problem with modified initial data and it converges to the given inviscid solution away from shock discontinuities as ε tends to zero. Convergence rates are given in terms of ε. The proof is given by a matched asymptotic analysis and a weighted elementary energy method.