Hyperbolic systems of balance laws via vanishing viscosity (Q817596)

Global weak solution of the Cauchy problem to a strictly hyperbolic system of balance laws \(u_{t}+f(u)_{x}+g(u)=0\) in one space dimension is constructed by the vanishing viscosity method. Under a suitable dissipativity assumptions on \(g(u),\) the viscous approximations \(u^{\varepsilon }\) converge for \(\varepsilon \rightarrow 0\) in \(L^{1}_{\text{loc}}\) to the admissible weak solution \(u.\) The small difference of initial data and constant equilibrium solution of the system is supposed.