Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws^★,★★

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
dqli@fudan.edu.cn
² School of Mathematical Sciences, Tongji University, Shanghai 200092, China

^a Corresponding author: yu_lei@tongji.edu.cn

Received: 24 April 2017
Revised: 16 August 2017
Accepted: 26 October 2017

Abstract

In this paper, we study the local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws with characteristics of constant multiplicity. We prove the two-sided boundary controllability, the one-sided boundary controllability and the two-sided boundary controllability with fewer controls, by applying the strategy used in [T. Li and L. Yu, J. Math. Pures et Appl. 107 (2017) 1–40; L. Yu, Chinese Ann. Math., Ser. B (To appear)]. Our constructive method is based on the well-posedness of semi-global solutions constructed by the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions, and on some further properties of both ε-approximate front tracking solutions and limit solutions.