Undercompressive shocks for a system of hyperbolic conservation laws with cubic nonlinearity
The author discussed the Riemann problem for the hyperbolic system \[ u_t-v_x=0, \qquad v_t-\sigma (u)_x =0 \] with \(\sigma (u) = u^3 +u\), which is monotone but nonconvex. It is proved that for all jump initial data, taking constant in \(x>0\) and \(x<0\) respectively, the Riemann problem has a unique solution, which consist of rarefaction waves and admissible shock waves.
scientific article; zbMATH DE number 1246319
scientific article