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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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Chinese Annals of Mathematics,Series B 2021年第5期42卷 643-676页

作者： Xing LU Tatsien LI School of Mathematics Southeast UniversityNanjing 211189China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematic Nonlinear Mathematical Modeling and Methods Laboratory

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.

关键词： First order linear hyperbolic system exact boundary controllability exact boundary observability Constructive method

exact boundary controllability for the Spatial Vibration of String with Dynamical boundary Conditions

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Chinese Annals of Mathematics,Series B 2020年第3期41卷 325-334页

作者： Yue WANG Günter LEUGERING Tatsien LI Department of Mathematics Friedrich-Alexander UniversityErlangen 91058GermanySchool of Mathematical SciencesFudan UniversityShanghai 200433China Department of Mathematics Friedrich-Alexander UniversityErlangen-NurembergCauerstrasse 1191058 ErlangenGermany School of Mathematical Sciences Fudan UniversityShajighai 200433ChinaShanghai Key Laboratory for Contemporary Applied MathematicNonlinear Mathematical Modeling and Methods Laboratory

This paper deals with the spatial vibration of an elastic string with masses at the endpoints. The authors derive the corresponding quasilinear wave equation with dynamical boundary conditions, and prove the exact bou... 详细信息

关键词： Spatial vibration of a string exact boundary controllability Dynamical boundary condition

exact boundary controllability FOR HIGHER ORDER QUASILINEAR HYPERBOLIC EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 2005年第2期20卷 127-141页

作者： YuLixin Dept.ofMath.andInform.Sci. YantaiUniv.Yantai264005China

By means of the existence and uniqueness of semi-global C1 solution to the mixed initial-boundary value problem with general nonlinear boundary conditions for first order quasilinear hyperbolic systems with zero eigen... 详细信息

关键词： semi-global C^1 solution exact boundary controllability higher order quasilinear hyperbolic system.

exact boundary controllability of Nodal Profile for Hyperbolic Systems

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Journal of Mathematical Research with Applications 2019年第6期39卷 554-562页

作者： Tatsien LI School of Mathematical Sciences Fudan University

In this survey paper we first recall the known results on the exact boundary controllability of nodal profile, then give some suggestions on further studies on this subject.

关键词： exact boundary controllability exact boundary controllability of nodal profile exact boundary controllability of partial nodal profile quasilinear hyperbolic system classical solution entropy solution asymptotic stability

One-side exact boundary controllability for First Order Quasilinear Hyperbolic Systems

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One-side Exact Boundary Controllability for First Order Quas...

第二十九届中国控制会议

作者： YU Lixin School of Mathematics and Information Sciences,Yantai University,Yantai 264005,Shandong,P.R.China

By a constructive method,we establish the local exact boundary controllability for first order quasilinear hyperbolic systems of diagonal form with boundary conditions in which the diagonal variables corresponding to ... 详细信息

关键词： exact boundary controllability Quasilinear Hyperbolic System Mixed Initial-boundary Value Problem

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一个一维二阶拟线性双曲组的精确边界能控性

Chinese Quarterly Journal of Mathematics 2023年第4期38卷 424-440页

作者：王珂潘盼盼 Department of Mathematics Donghua UniversityShanghai 201620China Institute for Nonlinear Sciences Donghua UniversityShanghai 201620China

In this paper,we propose a second-order quasilinear hyperbolic *** means of the theory on semi-global C^(1)solution to first-order quasilinear hyperbolic systems,we establish the existence and uniqueness of semi-global C^(2)solution to this second-order quasilinear hyperbolic *** then,the general constructive framework is utilized to obtain the local exact boundary controllability for this second-order system.

关键词： First-order quasilinear hyperbolic system Second-order quasilinear hyper-bolic system Semi-global solution exact boundary controllability

exact boundary Synchronization by Groups for a Kind of System of Wave Equations Coupled with Velocities

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Chinese Annals of Mathematics,Series B 2023年第1期44卷 17-34页

作者： Xing LU Tatsien LI School of Mathematics Southeast UniversityNanjing 211189China School of Mathematical Sciences Fudan UniversityShanghai 200433China Shanghai Key Laboratory for Contemporary Applied Mathematic Fudan UniversityShanghai 200433China Nonlinear Mathematical Modeling and Methods Laboratory Fudan UniversityShanghai 200433China

This paper deals with the exact boundary controllability and the exact boundary synchronization for a 1-D system of wave equations coupled with *** problems can not be solved directly by the usual HUM method for wave equations,however,by transforming the system into a first order hyperbolic system,the HUM method for 1-D first order hyperbolic systems,established by Li-Lu(2022)and Lu-Li(2022),can be applied to get the corresponding results.

关键词： exact boundary controllability exact boundary synchronization Coupled system of wave equations HUM method

NUMERICAL RECONSTRUCTION OF SMALL PERTURBATIONS IN THE ELECTROMAGNETIC COEFFICIENTS OF A DIELECTRIC MATERIAL

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Journal of Computational Mathematics 2014年第1期32卷 21-38页

作者： Marion Darbas Stephanie Lohrengel LAMFA UMR CNRS 7252 - Universitd de Picardie Jules Verne Amiens France LMR EA 4535 - Universitd de Reims Champagne-Ardenne Reims France

The aim of this paper is to solve numerically the inverse problem of reconstructing small amplitude perturbations in the magnetic permeability of a dielectric material from partial or total dynamic boundary measurements. Our numerical algorithm is based on the resolution of the time-dependent Maxwell equations, an exact controllability method and Fourier inversion for localizing the perturbations. Two-dimensional numerical experiments illustrate the performance of the reconstruction method for different configurations even in the case of limited-view data.

关键词： Maxwell's equations Inverse problems Numerical reconstruction exact boundary controllability Fourier inversion.