Exact and optimal controllability for scalar conservation laws with discontinuous flux
arXiv:2009.13324
Abstract
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been described to obtain the reachable set. Regarding the optimal control problem we first prove the existence of a minimizer and then the backward algorithm allows us to compute it. The same method also applies to compute the initial data control for an exact control problem. Our methodology for the proof relies on the explicit formula for the conservation laws with the discontinuous flux and finer properties of the characteristics curves.
It is to be noted most of the ideas and technical details was in the arxiv version arXiv:1603.01473 but that there was a gap in the proof, because the reflected characteristics was not being considered and hence the definition of the reachable set was incomplete. In this present version we fill this gap in subsection 3.3 and present a modified version