Volume 24, Number 2, April–June 2018
|Page(s)||793 - 810|
|Published online||13 June 2018|
Local exact boundary controllability of entropy solutions to linearly degenerate quasilinear hyperbolic systems of conservation laws★,★★
School of Mathematical Sciences, Fudan University,
2 School of Mathematical Sciences, Tongji University, Shanghai 200092, China
a Corresponding author: firstname.lastname@example.org
Revised: 16 August 2017
Accepted: 26 October 2017
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.
Mathematics Subject Classification: 95B05 / 35L60 / 35L65
Key words: Linearly degenerate quasilinear hyperbolic systems of conservation laws / local exact boundary controllability / semi-global entropy solutions / ε-approximate front tracking solutions
© EDP Sciences, SMAI 2018
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