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Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — The Constructive Method

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Abstract

In this paper the authors first present the definition and some properties of weak solutions to 1-D first order linear hyperbolic systems. Then they show that the constructive method with modular structure originally given in the framework of classical solutions is still very powerful and effective in the framework of weak solutions to prove the exact boundary (null) controllability and the exact boundary observability for first order hyperbolic systems.

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Author information

Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, 211189, China

    Xing Lu

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Tatsien Li

  3. Nonlinear Mathematical Modeling and Methods Laboratory, Shanghai Key Laboratory for Contemporary Applied Mathematic, Shanghai, China

    Tatsien Li

Authors
  1. Xing Lu
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  2. Tatsien Li
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Corresponding authors

Correspondence to Xing Lu or Tatsien Li.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11831011, 11901082), the Natural Science Foundation of Jiangsu Province (No. BK20190323) and the Fundamental Research Funds for the Central Universities of China.

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Lu, X., Li, T. Exact Boundary Controllability of Weak Solutions for a Kind of First Order Hyperbolic System — The Constructive Method. Chin. Ann. Math. Ser. B 42, 643–676 (2021). https://doi.org/10.1007/s11401-021-0284-3

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  • DOI: https://doi.org/10.1007/s11401-021-0284-3

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