Local exact boundary controllability of entropy solutions to a class of hyperbolic systems of conservation laws

TL;DR

This paper establishes the local exact boundary controllability of entropy solutions for a class of linearly degenerate hyperbolic conservation laws, extending classical methods with new constructive approaches.

Contribution

It introduces a novel constructive method for boundary controllability of entropy solutions, adapting classical strategies with essential modifications for this class of systems.

Findings

Proves two-sided boundary controllability.

Demonstrates controllability with fewer controls.

Establishes well-posedness of semi-global solutions.

Abstract

In this paper, we study the local exact boundary controllability of entropy solutions to a class linearly degenerate hyperbolic systems of conservation laws with constant multiplicity. The authors prove the two-sided boundary controllability, one-sided boundary controllability and two-sided controllability with less controls, by applying the strategy used originally for classical solutions with essential modifications. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of $ \e $-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions and some further properties on both $ \e $-approximate front tracking solutions and entropy solutions.