Authors abstract : Existence and admissibilityof shock solutions is discussed for the non-convex srictly hyperbolic system of equations
The system is fully nonlinear, i.e. it is nonlinear with respect to both unknows, and it does not admit the classical Lax-admissible solution for certain Riemann problems. By introducing complex-valued corrections in the framework of the weak asymptotic method, we show that a compressive shock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. In deed, in this context, we can show that every 22 system of conservation laws admits shock solutions.