Relaxation limit for piecewise smooth solutions to systems of conservation laws
The author shows that any piecewise smooth solution \(u^0(x,t)\) of the equation \(u_t+f(u)_x=0\), \((x\in \mathbb{R}^n)\) with finitely many noninteracting shocks satisfying the entropy condition is a strong limit (as \(\varepsilon \rightarrow 0\)) of solutions \(u^{\varepsilon }(x,t)\) of the system \(u_t+v_x=0\), \(v_t+au_x=-{1\over \varepsilon }(v-f(u))\), \( u,v\in \mathbb{R}^n.\)
scientific article; zbMATH DE number 1437341