On the Global Controllability of Scalar Conservation Laws with Boundary and Source Controls

We provide local and global controllability results for hyperbolic conservation laws on a bounded domain, with a general (not necessarily convex) flux and a time dependent source term acting as a control. The results are achieved for possibly critical states, both continuously differentiable states and BV states. The proofs are based on a combination of the return method and on the analysis of the Riccati equation for the space derivative of the solution