Local exact one-sided boundary null controllability of entropy solutions to a class of hyperbolic systems of balance laws

TL;DR

This paper proves the local exact one-sided boundary null controllability for entropy solutions of certain hyperbolic systems of balance laws with source terms, extending previous results for conservation laws.

Contribution

It introduces a modified constructive method using two types of approximate solutions to handle systems with source terms.

Findings

Established local boundary null controllability for systems with source terms.

Extended previous conservation law results to more general hyperbolic systems.

Developed a new approach with approximate solutions for control problems.

Abstract

We consider nxn hyperbolic systems of balance laws in one-space dimension under the assumption that all negative (resp. positive) characteristics are linearly degenerate. We prove the local exact one-sided boundary null controllability of entropy solutions to this class of systems, which generalizes the corresponding results from the case without source terms to that with source terms. In order to apply the strategy used for conservation law, we essentially modify the constructive method by introducing two different kinds of approximate solutions to system in the forward sense and to the system in the rightward (resp. leftward) sense, respectively, and we prove that their limit solutions are equivalent to some extend.