On the well-posedness and regularity of the wave equation with variable coefficients

被引：16

作者：

Guo, Bao-Zhu ^{[1
]}

Zhang, Zhi-Xiong

机构：

[1] Acad Sinica, Acad Math & Syst Sci, Beijing 100080, Peoples R China

[2] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

[3] Grad Univ Chinese Acad Sci, Beijing 100049, Peoples R China

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2007年 / 13卷 / 04期

关键词：

wave equation; transfer function; well-posed and regular system; boundary control and observation;

D O I：

10.1051/cocv:2007040

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

An open- loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well- posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.

引用

页码：776 / 792

页数：17

共 50 条

[1] The well-posedness and regularity of the Euler-Bernoulli equation with variable coefficients
Zhang, Zhi-Xiong
Guo, Bao-Zhu
2006 CHINESE CONTROL CONFERENCE, VOLS 1-5, 2006, : 2246 - +
[2] On well-posedness, regularity and exact controllability for problems of transmission of plate equation with variable coefficients
Guo, Bao-Zhu
Shao, Zhi-Chao
QUARTERLY OF APPLIED MATHEMATICS, 2007, 65 (04) : 705 - 736
[3] Low regularity well-posedness for the viscous surface wave equation
Xiaoxia Ren
Zhaoyin Xiang
Zhifei Zhang
Science China Mathematics, 2019, 62 : 1887 - 1924
[4] Low regularity well-posedness for the viscous surface wave equation
Xiaoxia Ren
Zhaoyin Xiang
Zhifei Zhang
ScienceChina(Mathematics), 2019, 62 (10) : 1887 - 1924
[5] Low regularity well-posedness for the viscous surface wave equation
Ren, Xiaoxia
Xiang, Zhaoyin
Zhang, Zhifei
SCIENCE CHINA-MATHEMATICS, 2019, 62 (10) : 1887 - 1924
[6] WELL-POSEDNESS OF WAVE EQUATION WITH A VARIABLE COEFFICIENT BY METHOD OF CHARACTERISTICS
Nakagawa, Nao
Yagi, Shintaro
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (05): : 2408 - 2415
[7] THE WELL-POSEDNESS AND REGULARITY OF A ROTATING BLADES EQUATION
Shen, Lin
Wang, Shu
Wang, Yongxin
ELECTRONIC RESEARCH ARCHIVE, 2020, 28 (02): : 691 - 719
[8] On the well-posedness for the nonlinear radial Schrodinger equation with spatial variable coefficients
Zheng, Bo-wen
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2019, 182 : 1 - 19
[9] Well-posedness and regularity for an Euler–Bernoulli plate with variable coefficients and boundary control and observation
Bao-Zhu Guo
Zhi-Xiong Zhang
Mathematics of Control, Signals, and Systems, 2007, 19 : 337 - 360
[10] GLOBAL WELL-POSEDNESS FOR THE KAWAHARA EQUATION WITH LOW REGULARITY
Kato, Takamori
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (03) : 1321 - 1339

← 1 2 3 4 5 →