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

Abstract

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.

On the global controllability of scalar conservation laws with boundary and source controls

“…The advantage of this construction is that we obtain the source control and the corresponding solution as limit of regular solutions which are easier to handle than the piecewise constant front tracking solutions employed in [38]. In fact, we rely on the approach developed in the present paper to address similar problems of global controllability for diagonal systems of conservation laws in the forthcoming paper [8].…”