On the nature of bifurcations of solutions of the Riemann problem for the truncated Euler system

For the truncated Euler system, we study the problem of local reachability of points of the state space. We construct bifurcations of one-front solutions of the truncated Euler system into two-front solutions. The truncated Euler system is an example of a nonstrictly hyperbolic system of conservation laws for which there is no complete basis of eigenvectors on the critical manifold (of multiple eigenvalues) and there exists an associated vector. The constructed bifurcations of critical shock waves give an answer to the Lax problem on the behavior of a shock wave after it passes through the critical manifold in the phase space.