Exact boundary controllability for 1-D quasilinear hyperbolic systems with a vanishing characteristic speed

TL;DR

This paper extends the theory of boundary controllability for 1-D quasilinear hyperbolic systems to cases with vanishing characteristic speeds, using the return method to recover controllability.

Contribution

It introduces a novel approach to achieve exact boundary controllability despite vanishing characteristic speeds in hyperbolic systems.

Findings

Established controllability results for systems with vanishing speeds

Applied the method to important models in the field

Demonstrated the effectiveness of the return method in this context

Abstract

The general theory on exact boundary controllability for general first order quasilinear hyperbolic systems requires that the characteristic speeds of system do not vanish. This paper deals with exact boundary controllability, when this is not the case. Some important models are also shown as applications of the main result. The strategy uses the return method, which allows in certain situations to recover non zero characteristic speeds.