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
Fabio Ancona;
2021
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.
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