数学季刊 ›› 2023, Vol. 38 ›› Issue (4): 424-440.doi: 10.13371/j.cnki.chin.q.j.m.2023.04.010

• • 上一篇    

一个一维二阶拟线性双曲组的精确边界能控性

  

  1. 1. Department of Mathematics, Donghua University, Shanghai 201620, China; 2. Institute for
    Nonlinear Sciences, Donghua University, Shanghai 201620, China
  • 收稿日期:2023-10-09 出版日期:2023-12-30 发布日期:2023-12-30
  • 通讯作者: : WANG Ke (1987-), female, native of Shangqiu, Henan, associate professor of Donghua University, engages in partial differential equation; E-mail: kwang@dhu.edu.cn
  • 作者简介: WANG Ke (1987-), female, native of Shangqiu, Henan, associate professor of Donghua University, engages in partial differential equation; PAN Pan-pan (2000-), female, native of Chizhou, Anhui, master of Donghua University, engages in partial differential equation.
  • 基金资助:
    Supported by the Science and Technology Commission of Shanghai Municipality (Grant No.
    23ZR1402100) and the Fundamental Research Funds for the Central Universities (Grant Nos. 2232022G-13 and
    2232023G-13).

Exact Boundary Controllability for a 1-D Second-Order Quasilinear Hyperbolic System

  1. 1. Department of Mathematics, Donghua University, Shanghai 201620, China; 2. Institute for
    Nonlinear Sciences, Donghua University, Shanghai 201620, China
  • Received:2023-10-09 Online:2023-12-30 Published:2023-12-30
  • Contact: : WANG Ke (1987-), female, native of Shangqiu, Henan, associate professor of Donghua University, engages in partial differential equation; E-mail: kwang@dhu.edu.cn
  • About author: WANG Ke (1987-), female, native of Shangqiu, Henan, associate professor of Donghua University, engages in partial differential equation; PAN Pan-pan (2000-), female, native of Chizhou, Anhui, master of Donghua University, engages in partial differential equation.
  • Supported by:
    Supported by the Science and Technology Commission of Shanghai Municipality (Grant No.
    23ZR1402100) and the Fundamental Research Funds for the Central Universities (Grant Nos. 2232022G-13 and
    2232023G-13).

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摘要：  In this paper, we propose a second-order quasilinear hyperbolic system. By
means of the theory on semi-global C1solution to first-order quasilinear hyperbolic
systems, we establish the existence and uniqueness of semi-global C2solution to this
second-order quasilinear hyperbolic system. After then, the general constructive framework
is utilized to obtain the local exact boundary controllability for this second-order system.
Keywords: First-order quasilinear hyperbolic system; Second-order quasilinear hyperbolic system; Semi-global solution; Exact boundary controllability

关键词: First-order quasilinear hyperbolic system, Second-order quasilinear hyperbolic system, Semi-global solution, Exact boundary controllability

Abstract:  In this paper, we propose a second-order quasilinear hyperbolic system. By
means of the theory on semi-global C1solution to first-order quasilinear hyperbolic
systems, we establish the existence and uniqueness of semi-global C2solution to this
second-order quasilinear hyperbolic system. After then, the general constructive framework
is utilized to obtain the local exact boundary controllability for this second-order system.
Keywords: First-order quasilinear hyperbolic system; Second-order quasilinear hyperbolic system; Semi-global solution; Exact boundary controllability

Key words: First-order quasilinear hyperbolic system, Second-order quasilinear hyperbolic system, Semi-global solution, Exact boundary controllability

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