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

TL;DR

This paper establishes global and semi-global controllability results for hyperbolic conservation laws with boundary and source controls, applicable to a broad class of flux functions and states, using advanced analytical techniques.

Contribution

It introduces new controllability results for scalar conservation laws with general flux and time-dependent source controls, extending previous work to non-convex fluxes and BV states.

Findings

Achieves controllability for both smooth and BV states.

Utilizes a novel combination of the return method and Riccati equation analysis.

Provides results for possibly critical states with non-convex fluxes.

Abstract

We provide global and semi-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, 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 equaiton for the space derivative of the solution.