Exact and optimal controllability for scalar conservation laws with discontinuous flux

TL;DR

This paper investigates the exact controllability of scalar 1-D conservation laws with discontinuous flux, establishing existence of optimal controls and providing algorithms for their computation based on explicit formulas and characteristic properties.

Contribution

It introduces a novel approach to optimal control for conservation laws with discontinuous flux, including existence proofs and computational algorithms.

Findings

Existence of a minimizer for the control problem

Algorithm for computing optimal control and initial data control

Explicit formulas and characteristic analysis underpin the method

Abstract

This paper deals with an optimal control problem and describes the reachable set for the scalar 1-D conservation laws with discontinuous flux. Regarding the optimal control problem we first prove the existence of a minimizer and then we prescribe an algorithm to compute it. The same method also applies to compute the initial data control. The proof relies on the explicit formula for the conservation laws with the discontinuous flux and finer properties of the characteristics.