Uniqueness and continuous dependence for systems of balance laws with dissipation (Q1599959)

This paper is devoted to study the Cauchy problem for strictly hyperbolic systems of balance laws \[ \begin{cases} u_t+f(u)_x=g(u),\\ u(0,x)=u_0, \end{cases} \tag{1} \] where \(x\in\mathbb{R}\), \(u(t,x)\in\mathbb{R}^n\), \(f,g:\Omega\to \mathbb{R}^n\), \(\Omega\) is an open neighborhood of the origin. The system (1) is assumed to be strictly hyperbolic, with each characteristic field either genuinely nonlinear or linearly degenerate; moreover is assumed that \(g\in C^2\), \(g(0)=0\). The authors deal with the uniqueness and continuous dependence from initial data of the solutions of (1).