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.