\(L^1\) continuous dependence property for systems of conservation laws (Q1973866)

This paper is devoted to the discontinuous solutions of the Cauchy problem for a hyperbolic system of conservation laws: \[ \partial_tu+\partial_xf(u)=0,\quad u(x,t)\in{\mathcal U},\tag{1} \] where \(\mathcal U\) is an open subset of \(\mathbb{R}^N\) and the flux-function \(f:{\mathcal U}\to\mathbb{R}^N\) is smooth and strictly hyperbolic. The authors study the uniqueness and \(L^1\) continuous dependence of entropy solutions for (1).