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

WANG Ke, PAN Pan-pan

doi:10.13371/j.cnki.chin.q.j.m.2023.04.010

Chinese Quarterly Journal of Mathematics >

2023 , Vol. 38 >Issue 4: 424 - 440

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.04.010

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

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1. Department of Mathematics, Donghua University, Shanghai 201620, China; 2. Institute for
Nonlinear Sciences, Donghua University, Shanghai 201620, China

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.

Received date: 2023-10-09

Online published: 2023-12-30

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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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

Cite this article

WANG Ke, PAN Pan-pan . Exact Boundary Controllability for a 1-D Second-Order Quasilinear Hyperbolic System[J]. Chinese Quarterly Journal of Mathematics, 2023 , 38(4) : 424 -440 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.04.010

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