Boundary control for transport equations

This paper considers two types of boundary control problems for linear transport equations. The first one shows that solutions on a subdomain domain $ X can be controlled exactly from incoming conditions under appropriate convexity assumptions. is in contrast with the only approximate typically obtains elliptic equations by an application unique continuation property, property which we prove does not hold We also consider outgoing solution conditions, notion similar to Dirichlet-to-Neumann map show well-chosen coefficients equation, this may possible. In such situations and (Fredholm) duality, obtain existence non-trivial are compatible vanishing conditions.