One-sided exact boundary null controllability of entropy solutions to a class of hyperbolic systems of conservation laws

详细信息    查看全文

• 作者：Tatsien Li^a ; ¹ ; ^{dqli@fudan.edu.cn} ; Lei Yu^b ; ² ; ^{yulei@fudan.edu.cn}
• 关键词：35L60 ; 35L65 ; 35B37
• 刊名：Journal de Mathématiques Pures et Appliquées
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：107
• 期：1
• 页码：1-40
• 全文大小：788 K
• 卷排序：107

文摘

In this paper, the one-sided exact boundary null controllability of entropy solutions is studied for a class of general strictly hyperbolic systems of conservation laws, whose negative (or positive) characteristic families are all linearly degenerate. The authors first prove the well-posedness of semi-global solutions constructed as the limit of ε-approximate front tracking solutions to the mixed initial-boundary value problem with general nonlinear boundary conditions and they establish various properties of both the ε-approximate front tracking solutions and such solutions. By means of essential modifications of the strategy suggested by the first author in [17] originally for the local exact boundary controllability in the framework of classical solutions, the one-sided local exact boundary null controllability of entropy solutions can then be realized via boundary controls acting on one side of the boundary, where the incoming characteristics are all linearly degenerate.